BuyFind*launch*

8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285740621

Chapter 12.5, Problem 38E

Textbook Problem

**23–40** Find an equation of the plane.

The plane that passes through the points

Calculus (MindTap Course List)

Ch. 12.1 - Suppose you start at the origin, move along the...Ch. 12.1 - Sketch the points (1,5,3),(0,2,3),(3,0,2), and...Ch. 12.1 - Which of the points A(4,0,1),B(3,1,5), and...Ch. 12.1 - What are the projections of the point 2, 3, 5 on...Ch. 12.1 - What does the equation x=4 represent in 2? What...Ch. 12.1 - What does the equation y = 3 represent in 3? What...Ch. 12.1 - Describe and sketch the surface in 3 represented...Ch. 12.1 - Describe and sketch the surface in 3 represented...Ch. 12.1 - Find the lengths of the sides of the triangle PQR....Ch. 12.1 - Find the lengths of the sides of the triangle PQR....

Ch. 12.1 - Determine whether the points lie on a straight...Ch. 12.1 - Find the distance from (4,2,6) to each of the...Ch. 12.1 - Find an equation of the sphere with centre (3,2,5)...Ch. 12.1 - Find an equation of the sphere with centre (2,6,4)...Ch. 12.1 - Find an equation of the sphere that passes through...Ch. 12.1 - Find an equation of the sphere that passes through...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - Show that the equation represents a sphere, and...Ch. 12.1 - a Prove that the midpoint of the line segment from...Ch. 12.1 - Find an equation of a sphere if one of its...Ch. 12.1 - Find equations of the spheres with centre (2,3,6)...Ch. 12.1 - Find an equation of the largest sphere with centre...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Describe in words the region of 3 represented by...Ch. 12.1 - Write inequalities to describe the region. The...Ch. 12.1 - Write inequalities to describe the region. The...Ch. 12.1 - Write inequalities to describe the region. The...Ch. 12.1 - Write inequalities to describe the region. The...Ch. 12.1 - The figure shows a line L1 in space and a second...Ch. 12.1 - Consider the points P such that the distance from...Ch. 12.1 - Find an equation of the set of all points...Ch. 12.1 - Find the volume of the solid that lies inside both...Ch. 12.1 - Find the distance between the spheres x2+y2+z2=4...Ch. 12.1 - Describe and sketch a solid with the following...Ch. 12.2 - Are the following quantities vectors or scalars?...Ch. 12.2 - What is the relationship between the point 4, 7...Ch. 12.2 - Name all the equal vectors in the parallelogram...Ch. 12.2 - Write each combination of vectors as a single...Ch. 12.2 - Copy the vectors in the figure and use them to...Ch. 12.2 - Copy the vectors in the figure and use them to...Ch. 12.2 - In the figure, the tip of c and the tail of d are...Ch. 12.2 - If the vectors in the figure satisfy |u|=|v|=1 and...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find a vector a with representation given by the...Ch. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Find the sum of the given vectors and illustrate...Ch. 12.2 - Find a+b,4a+2b,|a|, and |ab|. a=3,4,b=9,1Ch. 12.2 - Find a+b,4a+2b,|a|, and |ab|. a=5i+3j,b=i2jCh. 12.2 - Find a+b,4a+2b,|a|, and |ab|. a=4i3j+2k,b=2i4kCh. 12.2 - Find a+b,4a+2b,|a|, and |ab|. a=8,1,4,b=5,2,1Ch. 12.2 - Find a unit vector that has the same direction as...Ch. 12.2 - Find a unit vector that has the same direction as...Ch. 12.2 - Find a unit vector that has the same direction as...Ch. 12.2 - Find the vector that has the same direction as...Ch. 12.2 - What is the angle between the given vector and the...Ch. 12.2 - What is the angle between the given vector and the...Ch. 12.2 - If v lies in the first quadrant and makes an angle...Ch. 12.2 - If a child pulls a sled through the snow on a...Ch. 12.2 - A quarterback throws a football with angle of...Ch. 12.2 - Find the magnitude of the resultant force and the...Ch. 12.2 - Find the magnitude of the resultant force and the...Ch. 12.2 - The magnitude of a velocity vector is called...Ch. 12.2 - A woman walks due west on the deck of a ship at 3...Ch. 12.2 - A crane suspends a 500-lb steel beam horizontally...Ch. 12.2 - A block-and-tackle pulley hoist is suspended in a...Ch. 12.2 - The tension T at each end of a chain has magnitude...Ch. 12.2 - A boatman wants to cross a canal that is 3 km wide...Ch. 12.2 - Three forces act on an object. Two of the forces...Ch. 12.2 - Find the unit vectors that are parallel to the...Ch. 12.2 - a Find the unit vectors that are parallel to the...Ch. 12.2 - If A, B, and C are the vertices of a triangle,...Ch. 12.2 - Let C be the point on the line segment AB that is...Ch. 12.2 - a Draw the vectors a=3,2,b=2,1 and c=7,1. b Show,...Ch. 12.2 - Suppose that a and b are nonzero vectors that are...Ch. 12.2 - If r=x,y,z and r0=x0,y0,z0, describe the set of...Ch. 12.2 - If r=x,y,r1=x1,y1, and r2=x2,y2, describe the set...Ch. 12.2 - Figure 16 gives a geometric demonstration of...Ch. 12.2 - Prove Property 5 of vectors algebraically for the...Ch. 12.2 - Use vectors to prove that the line joining the...Ch. 12.2 - Suppose the three coordinate planes are all...Ch. 12.3 - Which of the following expressions are meaningful?...Ch. 12.3 - 210 Find ab. a=5,2, b=3,4Ch. 12.3 - 210 Find ab. a=1.5,0.4, b=4,6Ch. 12.3 - 210 Find ab. a=6,2,3, b=2,5,1Ch. 12.3 - 210 Find ab. a=4,1,14, b=6,3,8Ch. 12.3 - 210 Find ab. a=p,p,2p, b=2q,q,qCh. 12.3 - 210 Find ab. a=2i+j, b=i-j+kCh. 12.3 - 210 Find ab. a=3i+2j-k, b=4i+5kCh. 12.3 - 210 Find ab. |a|=7, |b|=4, the angle between a and...Ch. 12.3 - Find ab. |a|=80, |b|=50, the angle between a and b...Ch. 12.3 - If u is a unit vector, find uv and uw.Ch. 12.3 - If u is a unit vector, find uv and uw.Ch. 12.3 - a Show that ij=jki=0. b Show that ii=jj=kk=1.Ch. 12.3 - A street vendor sells a hamburgers, b hot dogs,...Ch. 12.3 - Find the angle between the vectors. First find an...Ch. 12.3 - Find the angle between the vectors. First find an...Ch. 12.3 - Find the angle between the vectors. First find an...Ch. 12.3 - Find the angle between the vectors. First find an...Ch. 12.3 - Find the angle between the vectors. First find an...Ch. 12.3 - Find the angle between the vectors. First find an...Ch. 12.3 - 2122 Find, correct to the nearest degree, the...Ch. 12.3 - 2122 Find, correct to the nearest degree, the...Ch. 12.3 - 2324 Determine whether the given vectors are...Ch. 12.3 - 2324 Determine whether the given vectors are...Ch. 12.3 - Use vectors to decide whether the triangle with...Ch. 12.3 - Find the values of x such that the angle between...Ch. 12.3 - Find a unit vector that is orthogonal to both i+j...Ch. 12.3 - Find two unit vectors that make an angle of 60...Ch. 12.3 - 2930 Find the acute angle between the lines....Ch. 12.3 - 2930 Find the acute angle between the lines....Ch. 12.3 - 3132 Find the acute angles between the curves at...Ch. 12.3 - 3132 Find the acute angles between the curves at...Ch. 12.3 - 3337 Find the direction cosines and direction...Ch. 12.3 - 3337 Find the direction cosines and direction...Ch. 12.3 - 3337 Find the direction cosines and direction...Ch. 12.3 - 3337 Find the direction cosines and direction...Ch. 12.3 - 3337 Find the direction cosines and direction...Ch. 12.3 - If a vector has direction angles =/4 and =/3, find...Ch. 12.3 - 3944 Find the scalar and vector projections of b...Ch. 12.3 - 3944 Find the scalar and vector projections of b...Ch. 12.3 - Find the scalar and vector projections of b onto...Ch. 12.3 - Find the scalar and vector projections of b onto...Ch. 12.3 - Find the scalar and vector projections of b onto...Ch. 12.3 - Find the scalar and vector projections of b onto...Ch. 12.3 - Show that the vector orthaab=bprojba is orthogonal...Ch. 12.3 - For the vectors in Exercise 40, find orthab and...Ch. 12.3 - If a=3,0,1, find a vector b such that compab=2.Ch. 12.3 - Suppose that a and b are nonzero vectors. a Under...Ch. 12.3 - Find the work done by a force F=8i6j+9k that moves...Ch. 12.3 - A tow truck drags a stalled car along a road. The...Ch. 12.3 - A sled is pulled along a level path through snow...Ch. 12.3 - A boat sails south with the help of a wind blowing...Ch. 12.3 - Use a scalar projection to show that the distance...Ch. 12.3 - If r=x,y,z,a=a1,a2,a3, and b=b1,b2,b3, show that...Ch. 12.3 - Find the angle between a diagonal of a cube and...Ch. 12.3 - Find the angle between a diagonal of a cube and a...Ch. 12.3 - A molecule of methane, CH4, is structured with the...Ch. 12.3 - If c=|a|b+|b|a, where a, b, and c are all nonzero...Ch. 12.3 - Prove Properties 2, 4, and 5 of the dot product...Ch. 12.3 - Suppose that all sides of a quadrilateral are...Ch. 12.3 - Use Theorem 3 to prove the Cauchy-Schwarz...Ch. 12.3 - The Triangle Inequality for vectors is...Ch. 12.3 - The Parallelogram Law states that...Ch. 12.3 - Show that if u+v and uv are orthogonal, then the...Ch. 12.3 - If is the angle between vectors a and b, show...Ch. 12.4 - 17 Find the cross product ab and verify that it is...Ch. 12.4 - 17 Find the cross product ab and verify that it is...Ch. 12.4 - 17 Find the cross product ab and verify that it is...Ch. 12.4 - 17 Find the cross product ab and verify that it is...Ch. 12.4 - 17 Find the cross product ab and verify that it is...Ch. 12.4 - 17 Find the cross product ab and verify that it is...Ch. 12.4 - 17 Find the cross product ab and verify that it is...Ch. 12.4 - If a=i2k and b=j+k, find ab. Sketch a, b, and ab....Ch. 12.4 - 912 Find the vector, not with determinants, but by...Ch. 12.4 - 912 Find the vector, not with determinants, but by...Ch. 12.4 - 912 Find the vector, not with determinants, but by...Ch. 12.4 - 912 Find the vector, not with determinants, but by...Ch. 12.4 - State whether each expression is meaningful. If...Ch. 12.4 - 1415 Find |uv| and determine whether uv is...Ch. 12.4 - 1415 Find |uv| and determine whether uv is...Ch. 12.4 - The figure shows a vector a in the xy-plane and a...Ch. 12.4 - If a=2,1,3 and b=4,2,1, find ab and ba.Ch. 12.4 - If a=1,0,1,b=2,1,1, and c=0,1,3, show that...Ch. 12.4 - Find two unit vectors orthogonal to both 3,2,1 and...Ch. 12.4 - Find two unit vectors orthogonal to both jk and...Ch. 12.4 - Show that 0a=0=a0 for any vector a in V3.Ch. 12.4 - Show that (ab)b=0 for all vectors a and b in V3.Ch. 12.4 - 2326 Prove the property of cross products Theorem...Ch. 12.4 - 2326 Prove the property of cross products Theorem...Ch. 12.4 - 2326 Prove the property of cross products Theorem...Ch. 12.4 - 2326 Prove the property of cross products Theorem...Ch. 12.4 - Find the area of the parallelogram with vertices...Ch. 12.4 - Find the area of the parallelogram with vertices...Ch. 12.4 - 2932 a Find a nonzero vector orthogonal to the...Ch. 12.4 - 2932 a Find a nonzero vector orthogonal to the...Ch. 12.4 - 2932 a Find a nonzero vector orthogonal to the...Ch. 12.4 - 2932 a Find a nonzero vector orthogonal to the...Ch. 12.4 - 3334 Find the volume of the parallelepiped...Ch. 12.4 - 3334 Find the volume of the parallelepiped...Ch. 12.4 - 3536 Find the volume of the parallelepiped with...Ch. 12.4 - 3536 Find the volume of the parallelepiped with...Ch. 12.4 - Use the scalar triple product to verify that the...Ch. 12.4 - Use the scalar triple product to determine whether...Ch. 12.4 - A bicycle pedal is pushed by a foot with a 60-N...Ch. 12.4 - a A horizontal force of 20 lb is applied to the...Ch. 12.4 - A wrench 30 cm long lies along the positive y-axis...Ch. 12.4 - Let v=5j and let u be a vector with length 3 that...Ch. 12.4 - If ab=3 and ab=1,2,2, find the angle between a and...Ch. 12.4 - a Find all vectors v such that 1,2,1v=3,1,5 b...Ch. 12.4 - a Let P be a point not on the line L that passes...Ch. 12.4 - a Let P be a point not on the plane that passes...Ch. 12.4 - Show that |ab|2=|a|2|b|2(ab)2.Ch. 12.4 - If a+b+c=0, show that ab=bc=caCh. 12.4 - Prove that (ab)(a+b)=2(ab).Ch. 12.4 - Prove Property 6 of cross products, that is,...Ch. 12.4 - Use Exercise 50 to prove that a(bc)+b(ca)+c(ab)=0Ch. 12.4 - Prove that (ab)(cd)=|acbcadbd|Ch. 12.4 - Suppose that a0. a If ab=ac, does it follow that...Ch. 12.4 - If v1, v2, and v3 are noncoplanar vectors, let...Ch. 12.5 - Determine whether each statement is true or false...Ch. 12.5 - 25 Find a vector equation and parametric equations...Ch. 12.5 - 25 Find a vector equation and parametric equations...Ch. 12.5 - 25 Find a vector equation and parametric equations...Ch. 12.5 - 25 Find a vector equation and parametric equations...Ch. 12.5 - 612 Find parametric equations and symmetric...Ch. 12.5 - 612 Find parametric equations and symmetric...Ch. 12.5 - 612 Find parametric equations and symmetric...Ch. 12.5 - 612 Find parametric equations and symmetric...Ch. 12.5 - 612 Find parametric equations and symmetric...Ch. 12.5 - 612 Find parametric equations and symmetric...Ch. 12.5 - 612 Find parametric equations and symmetric...Ch. 12.5 - Is the line through (4,6,1) and (2,0,3) parallel...Ch. 12.5 - Is the line through (2,4,0) and (1,1,1)...Ch. 12.5 - a Find symmetric equations for the line that...Ch. 12.5 - a Find parametric equations for the line through...Ch. 12.5 - Find a vector equation for the line segment from...Ch. 12.5 - Find parametric equations for the line segment...Ch. 12.5 - 1922 Determine whether the lines L1 and L2 are...Ch. 12.5 - 1922 Determine whether the lines L1 and L2 are...Ch. 12.5 - 1922 Determine whether the lines L1 and L2 are...Ch. 12.5 - 1922 Determine whether the lines L1 and L2 are...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane that...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane...Ch. 12.5 - 2340 Find an equation of the plane. The plane that...Ch. 12.5 - 2340 Find an equation of the plane. The plane that...Ch. 12.5 - 2340 Find an equation of the plane. The plane that...Ch. 12.5 - 2340 Find an equation of the plane. The plane that...Ch. 12.5 - 2340 Find an equation of the plane. The plane that...Ch. 12.5 - 2340 Find an equation of the plane. The plane that...Ch. 12.5 - 4144 Use intercepts to help sketch the plane....Ch. 12.5 - 4144 Use intercepts to help sketch the plane....Ch. 12.5 - 4144 Use intercepts to help sketch the plane....Ch. 12.5 - 4144 Use intercepts to help sketch the plane....Ch. 12.5 - 4547 Find the point at which the line intersects...Ch. 12.5 - 4547 Find the point at which the line intersects...Ch. 12.5 - 4547 Find the point at which the line intersects...Ch. 12.5 - Where does the line through (3,1,0) and (1,5,6)...Ch. 12.5 - Find direction numbers for the line of...Ch. 12.5 - Find the cosine of the angle between the planes...Ch. 12.5 - 5156 Determine whether the planes are parallel,...Ch. 12.5 - 5156 Determine whether the planes are parallel,...Ch. 12.5 - 5156 Determine whether the planes are parallel,...Ch. 12.5 - 5156 Determine whether the planes are parallel,...Ch. 12.5 - 5156 Determine whether the planes are parallel,...Ch. 12.5 - 5156 Determine whether the planes are parallel,...Ch. 12.5 - 5758 a Find parametric equations for the line of...Ch. 12.5 - 5758 a Find parametric equations for the line of...Ch. 12.5 - 5960 Find symmetric equations for the line of...Ch. 12.5 - 5960 Find symmetric equations for the line of...Ch. 12.5 - Find an equation for the plane consisting of all...Ch. 12.5 - Find an equation for the plane consisting of all...Ch. 12.5 - Find an equation of the plane with x-intercept a,...Ch. 12.5 - a Find the point at which the given lines...Ch. 12.5 - Find parametric equations for the line through the...Ch. 12.5 - Find parametric equations for the line through the...Ch. 12.5 - Which of the following four planes are parallel?...Ch. 12.5 - Which of the following four lines are parallel?...Ch. 12.5 - 6970 Use the formula in Exercise 12.4.45 to find...Ch. 12.5 - 6970 Use the formula in Exercise 12.4.45 to find...Ch. 12.5 - 7172 Find the distance from the point to the given...Ch. 12.5 - 7172 Find the distance from the point to the given...Ch. 12.5 - 7374 Find the distance between the given parallel...Ch. 12.5 - 7374 Find the distance between the given parallel...Ch. 12.5 - Show that the distance between the parallel planes...Ch. 12.5 - Find equations of the planes that are parallel to...Ch. 12.5 - Show that the lines with symmetric equations x=y=z...Ch. 12.5 - Find the distance between the skew lines with...Ch. 12.5 - Let L1 be the line through the origin and the...Ch. 12.5 - Let L1 be the line through the points (1,2,6) and...Ch. 12.5 - Two tanks are participating in a battle...Ch. 12.5 - Give a geometric description of each family of...Ch. 12.5 - If a, b, and c are not all 0, show that the...Ch. 12.6 - a What does the equation y=x2 represent as a curve...Ch. 12.6 - a Sketch the graph of y=ex as a curve in 2. b...Ch. 12.6 - 38 Describe and sketch the surface. x2+z2=1Ch. 12.6 - 38 Describe and sketch the surface. 4x2+y2=4Ch. 12.6 - 38 Describe and sketch the surface. z=1y2Ch. 12.6 - 38 Describe and sketch the surface. y=z2Ch. 12.6 - 38 Describe and sketch the surface. xy=1Ch. 12.6 - 38 Describe and sketch the surface. z=sinyCh. 12.6 - a Find and identify the traces of the quadric...Ch. 12.6 - a Find and identify the traces of the quadric...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 1120 Use traces to sketch and identify the...Ch. 12.6 - 2128 Match the equation with reasons for your...Ch. 12.6 - 2128 Match the equation with reasons for your...Ch. 12.6 - 2128 Match the equation with reasons for your...Ch. 12.6 - 2128 Match the equation with reasons for your...Ch. 12.6 - 2128 Match the equation with reasons for your...Ch. 12.6 - 2128 Match the equation with reasons for your...Ch. 12.6 - 2128 Match the equation with reasons for your...Ch. 12.6 - 2128 Match the equation with reasons for your...Ch. 12.6 - 2930 Sketch and identify a quadric surface that...Ch. 12.6 - 2930 Sketch and identify a quadric surface that...Ch. 12.6 - 3138 Reduce the equation to one of the standard...Ch. 12.6 - 3138 Reduce the equation to one of the standard...Ch. 12.6 - 3138 Reduce the equation to one of the standard...Ch. 12.6 - 3138 Reduce the equation to one of the standard...Ch. 12.6 - 3138 Reduce the equation to one of the standard...Ch. 12.6 - 3138 Reduce the equation to one of the standard...Ch. 12.6 - 3138 Reduce the equation to one of the standard...Ch. 12.6 - 3138 Reduce the equation to one of the standard...Ch. 12.6 - 3942 Use a computer with three-dimensional...Ch. 12.6 - 3942 Use a computer with three-dimensional...Ch. 12.6 - 3942 Use a computer with three-dimensional...Ch. 12.6 - 3942 Use a computer with three-dimensional...Ch. 12.6 - Sketch the region bounded by the surfaces z=x2+y2...Ch. 12.6 - Sketch the region bounded by the paraboloids...Ch. 12.6 - Find an equation for the surface obtained by...Ch. 12.6 - Find an equation for the surface obtained by...Ch. 12.6 - Find an equation for the surface consisting of all...Ch. 12.6 - Find an equation for the surface consisting of all...Ch. 12.6 - Traditionally, the earths surface has been modeled...Ch. 12.6 - A cooling tower for a nuclear reactor is to be...Ch. 12.6 - Show that if the point (a,b,c) lies on the...Ch. 12.6 - Show that the curve of intersection of the...Ch. 12.6 - Graph the surfaces z=x2+y2 and z=1y2 on a common...Ch. 12.R - What is the difference between a vector and a...Ch. 12.R - How do you add two vectors geometrically? How do...Ch. 12.R - If a is a vector and c is a scalar, how is ca...Ch. 12.R - How do you find the vector from one point to...Ch. 12.R - How do you find the dot product ab of two vectors...Ch. 12.R - How are dot products useful?Ch. 12.R - Write expressions for the scalar and vector...Ch. 12.R - How do you find the cross product ab of two...Ch. 12.R - How are cross products useful?Ch. 12.R - a How do you find the area of the parallelogram...Ch. 12.R - How do you find a vector perpendicular to a plane?Ch. 12.R - How do you find the angle between two intersecting...Ch. 12.R - Write a vector equation, parametric equations, and...Ch. 12.R - Write a vector equation and a scalar equation for...Ch. 12.R - a How do you tell if two vectors are parallel? b...Ch. 12.R - a Describe a method for determining whether three...Ch. 12.R - a How do you find the distance from a point to a...Ch. 12.R - What are the traces of a surface? How do you find...Ch. 12.R - Write equations in standard form of the six types...Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - Determine whether the statement is true or false....Ch. 12.R - a Find an equation of the sphere that passes...Ch. 12.R - Copy the vectors in the figure and use them to...Ch. 12.R - If u and v are the vectors shown in the figure,...Ch. 12.R - Calculate the given quantity if...Ch. 12.R - Find the values of x such that the vectors 3,2,x...Ch. 12.R - Find two unit vectors that are orthogonal to both...Ch. 12.R - Suppose that u(vw)=2. Find a (uv)w b u(wv) c v(uw)...Ch. 12.R - Show that if a, b, and c are in V3, then...Ch. 12.R - Find the acute angle between two diagonals of a...Ch. 12.R - Given the points...Ch. 12.R - a Find a vector perpendicular to the plane through...Ch. 12.R - A constant force F=3i+5j+10k moves an object along...Ch. 12.R - A boat is pulled onto shore using two ropes, as...Ch. 12.R - Find the magnitude of the torque about P if a 50-N...Ch. 12.R - 1517 Find parametric equations for the line. The...Ch. 12.R - 1517 Find parametric equations for the line. The...Ch. 12.R - 1517 Find parametric equations for the line. The...Ch. 12.R - 1820 Find an equation of the plane. The plane...Ch. 12.R - 1820 Find an equation of the plane. The plane...Ch. 12.R - 1820 Find an equation of the plane. The plane...Ch. 12.R - Find the point in which the line with parametric...Ch. 12.R - Find the distance from the origin to the line...Ch. 12.R - Determine whether the lines given by the symmetric...Ch. 12.R - a Show that the planes x+yz=1 and 2x3y+4z=5 are...Ch. 12.R - Find an equation of the plane through the fine of...Ch. 12.R - a Find an equation of the plane that passes...Ch. 12.R - Find the distance between the planes 3x+y4z=2 and...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - 28-36. Identify and sketch the graph of each...Ch. 12.R - An ellipsoid is created by rotating the ellipse...Ch. 12.R - A surface consists of all points P such that the...Ch. 12.P - Each edge of a cubical box has length 1 m. The box...Ch. 12.P - Let B be a solid box with length L, width W, and...Ch. 12.P - Let L be the line of intersection of the planes...Ch. 12.P - A plane is capable of flying at a speed of 180...Ch. 12.P - Suppose v1 and v2 are vectors with,...Ch. 12.P - Find an equation of the largest sphere that passes...Ch. 12.P - Suppose a block of mass m is placed on an inclined...Ch. 12.P - A solid has the following properties. When...

Find more solutions based on key concepts

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 5-8, graph the given function or equation. y=2x+5

Applied Calculus

Finding Derivatives In Exercises 2940, find the derivative of the function. f(x)=5

Calculus: An Applied Approach (MindTap Course List)

Find an equation of the plane. 30. The plane that contains the line x = 1 + t, y = 2 t, z = 4 3t and is paral...

Calculus: Early Transcendentals

Radicals and Exponents Write each radical expression using exponents, and each exponential expression using rad...

Precalculus: Mathematics for Calculus (Standalone Book)

Find the length of the curve. 6. r(t) = t2 i + 9t j + 4t3/2 k, 1 t 4

Multivariable Calculus

Maximum Area A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of ...

Calculus: Early Transcendental Functions

Calculate y'. 42. y=(x+)4x4+4

Single Variable Calculus: Early Transcendentals, Volume I

SW A large counseling center needs to evaluate several experimental programs. Write a paragraph summarizing the...

Essentials Of Statistics

What value is represented by the uppercase letter N? a. the number of scores in a population b. the number of s...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 1-8, use the graph of the given function f to determine limxaf(x) at the indicated value of a, if ...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard funct...

Single Variable Calculus

Residual Plot: Miles per Gallon Consider the data of Problem 9. (a) Make a residual plot for the least-squares ...

Understanding Basic Statistics

A random sample is selected from a normal population with a mean of =30and a standard deviation of =8 . After a...

Statistics for The Behavioral Sciences (MindTap Course List)

Expand each expression in Exercises 122. (x+yxy)2

Finite Mathematics

Circle P has a radius of length 8in. Points A, B, C, and D lie on circle P in such a way that mAPB=90 and mCPD=...

Elementary Geometry For College Students, 7e

21. Hargray Communications offered a bundled package of television cable, broadband Internet, and basic telepho...

Mathematical Applications for the Management, Life, and Social Sciences

In Exercises 19 to 26, show that the given set has a cardinality of K by establishing a one-to-one corresponden...

Mathematical Excursions (MindTap Course List)

Suppose that you have ten lightbulbs, that the lifetime of each is independent of all the other lifetimes, and ...

Probability and Statistics for Engineering and the Sciences

For Problems 51-78, simplify each of the numerical expressions. Objective 3 48(1411)(106)

Intermediate Algebra

A potato patch has 7 rows with 75 hills of potatoes per row. If each potato hill yields 3 lb of marketable pota...

Elementary Technical Mathematics

Find dy/dx and d2y/dx2. For which values of t is the curve concave upward? 13. x = et, y = tet

Single Variable Calculus: Early Transcendentals

Population Growth The rate of growth dP/dt of a population of bacteria is proportional to the square root of t,...

Calculus of a Single Variable

44. Let be a subgroup of a group .For, define the relation by
if and ...

Elements Of Modern Algebra

Multiply. (sin4)2

Trigonometry (MindTap Course List)

SECTION I – UNDERSTANDING AND WORKING WITH FRACTIONS
40. What fraction represents the laptops in this group of ...

Contemporary Mathematics for Business & Consumers

For

Study Guide for Stewart's Multivariable Calculus, 8th

Which is the best graph of y = f (x) for the given graph of y = f (x)? a) None of these

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Volume In Exercises 27 and 28, use a double integral in polar coordinates to find the volume of the solid bound...

Calculus: Early Transcendental Functions (MindTap Course List)

Given O with radii OA- and OB- and chord AB-. aWhat type of figure sector or segment is bounded by OA-, OB- and...

Elementary Geometry for College Students

What does the expected value of a game measure?

Finite Mathematics for the Managerial, Life, and Social Sciences

Finding a Binormal Vector In Exercises 47-52, find the vectors T and N and the binormal vector B=TN for the vec...

Calculus (MindTap Course List)

Finding the Principal Unit Normal Vector In Exercises 47-50, find the principal unit normal vector to the curse...

Multivariable Calculus

The graph of each function is a translation of the graph of fx=x3.Graph each function. hx=x+13-1

College Algebra (MindTap Course List)

Make a list of some of the factors in your life that change from one day to the next. Possible examples include...

Research Methods for the Behavioral Sciences (MindTap Course List)

In February 2012, the Pew Internet American Life project conducted a survey that included several questions ab...

Statistics for Business & Economics, Revised (MindTap Course List)

In Exercises 9-26, use the given information to draw a right triangle labeled like the one shown in Figure 8.89...

Mathematics: A Practical Odyssey

The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for aweekend is 600 or less. A m...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe the characteristics of a within-subjects experimental research design.

Research Methods for the Behavioral Sciences (MindTap Course List)

Suppose that the probability is 0.1 that any given citrus tree will show measurable damage when the temperature...

Introduction To Statistics And Data Analysis

In the following table, the diameters and heights of cones are given. Find the volumes of the cones. Round the ...

Mathematics For Machine Technology

23. Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in t...

Essentials Of Statistics For Business & Economics

Let G be a simple graph with n vertices. What is the relation between the number of edges of G and the number o...

Discrete Mathematics With Applications

Extracting Square Roots In Exercises 19-32, solve the equation by extracting square roots. When a solution is i...

College Algebra

Finding exponential formula In Exercise S-1 trough S-7, use the given information to find a formula for the exp...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

In Problems 116 the indicated function y1(x) is a solution of the given differential equation. Use reduction of...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

In a survey, 40 people were asked how many times per year they had their car in the shop for repairs. The resul...

Introductory Statistics

2. Consider the following hypothesis test.
The following results are for two independent samples taken from th...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)