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CalculusCalculus (MindTap Course List)23–40 Find an equation of the plane. The plane that passes through the points ( 0 , − 2 , 5 ) and ( − 1 , 3 , 1 ) and is perpendicular to the plane 2 z = 5 x + 4 y

23–40 Find an equation of the plane. The plane that passes through the points ( 0 , − 2 , 5 ) and ( − 1 , 3 , 1 ) and is perpendicular to the plane 2 z = 5 x + 4 y

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Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621
BuyFind

Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
Chapter 12.5, Problem 38E
Textbook Problem

23–40 Find an equation of the plane.

The plane that passes through the points ( 0 , − 2 , 5 ) and ( − 1 , 3 , 1 ) and is perpendicular to the plane 2 z = 5 x + 4 y

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Chapter 12.5,
Problem 37E
Chapter 12.5,
Problem 39E

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Chapter 12 Solutions

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...

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