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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275347

Chapter 11.2, Problem 26E

Textbook Problem

Finding the Distance Between Two Points in Space In Exercises 25–28. find the distance between the points.

(–1, 1, 1), (–3, 5, –3)

Calculus (MindTap Course List)

Ch. 11.1 - CONCEPT CHECK Scalar and Vector Describe the...Ch. 11.1 - CONCEPT CHECK Vector Two points and a vector are...Ch. 11.1 - Sketching a Vector In Exercises 3 and 4, (a) find...Ch. 11.1 - Sketching a Vector In Exercises 3 and 4, (a) find...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Writing a Vector in Different Forms In Exercises...

Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Writing a Vector in Different Forms to Exercises...Ch. 11.1 - Writing a Vector in Different Forms to Exercises...Ch. 11.1 - Writing a Vector in Different Forms to Exercises...Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Finding a Terminal Point In Exercise 17 and 18,...Ch. 11.1 - Finding a Terminal Point In Exercise 17 and 18,...Ch. 11.1 - Finding a Magnitude of a Vector In Exercises...Ch. 11.1 - Finding a Magnitude of a Vector In Exercises...Ch. 11.1 - Finding a Magnitude of a Vector In Exercises...Ch. 11.1 - Finding a Magnitude of a VectorIn Exercises 1924,...Ch. 11.1 - Finding a Magnitude of a VectorIn Exercises 1924,...Ch. 11.1 - Finding a Magnitude of a VectorIn Exercises 1924,...Ch. 11.1 - Sketching Scalar MultipliesIn Exercises 25 and 26,...Ch. 11.1 - Sketching Scalar MultipliesIn Exercises 25 and 26,...Ch. 11.1 - Using Vector Operations In Exercise 27 and 28, And...Ch. 11.1 - Using Vector Operations In Exercise 27 and 28, And...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Finding MagnitudesIn Exercises 3942, find the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Finding MagnitudesIn Exercises 3942, find the...Ch. 11.1 - Finding MagnitudesIn Exercises 3942, find the...Ch. 11.1 - Using the Triangle Inequality In Exercises 43 und...Ch. 11.1 - Using the Triangle Inequality In Exercises 43 und...Ch. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Finding a VectorIn Exercises 4952, find the...Ch. 11.1 - Finding a Vector In Exercises 49-52, find the...Ch. 11.1 - Finding a Vector In Exercises 49-52, find the...Ch. 11.1 - Finding a VectorIn Exercises 4952, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - EXPLORING CONCEPTS Think About ItIn Exercises 57...Ch. 11.1 - EXPLORING CONCEPTS Think About ItIn Exercises 57...Ch. 11.1 - EXPLORING CONCEPTS Triangle Consider a triangle...Ch. 11.1 - HOW DO YOU SEE IT? Use the figure to determine...Ch. 11.1 - Finding Values In Exercises 61-66, And a and b...Ch. 11.1 - Finding ValueIn Exercises 6166, find a and b such...Ch. 11.1 - Finding ValueIn Exercises 6166, find a and b such...Ch. 11.1 - Finding ValueIn Exercises 6166, find a and b such...Ch. 11.1 - Finding ValueIn Exercises 6166, find a and b such...Ch. 11.1 - Finding ValueIn Exercises 6166, find a and b such...Ch. 11.1 - Finding Unit VectorsIn Exercises 6772, find a unit...Ch. 11.1 - Finding Unit VectorsIn Exercises 6772, find a unit...Ch. 11.1 - Finding Unit Vectors In Exercises 67-72, find a...Ch. 11.1 - Finding Unit Vectors In Exercises 67-72, find a...Ch. 11.1 - Finding Unit Vectors In Exercises 67-72, find a...Ch. 11.1 - Finding Unit VectorsIn Exercises 6772, find a unit...Ch. 11.1 - Finding a Vector In Exercises 73 and 74, find the...Ch. 11.1 - Finding a Vector In Exercises 73 and 74, find the...Ch. 11.1 - Resultant ForceForces with magnitudes of 500...Ch. 11.1 - Numerical and Graphical Analysis Forces with...Ch. 11.1 - Resultant ForceThree forces with magnitudes of 75...Ch. 11.1 - Resultant ForceThree forces with the magnitudes of...Ch. 11.1 - Cable Tension In Exercises 79 and 80, determine...Ch. 11.1 - Cable TensionIn Exercises 79 and 80, determine the...Ch. 11.1 - Projectile Motion A gun with a muzzle velocity of...Ch. 11.1 - Shared Load To carry a 100-pound cylindrical...Ch. 11.1 - Navigation A plane is flying with a bearing of...Ch. 11.1 - NavigationA plane flies at a constant groundspeed...Ch. 11.1 - True or False? In Exercises 85-94, determine...Ch. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - True or False? In Exercises 85-94, determine...Ch. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - Proof Prove that u=(cos)i(sin)j and...Ch. 11.1 - GeometryUsing vectors, prove that the line segment...Ch. 11.1 - GeometryUsing vectors, prove that the diagonals of...Ch. 11.1 - Proof Prove that the vector w=uv+vu bisects the...Ch. 11.1 - Using a Vector Consider the vector u=x,y, Describe...Ch. 11.1 - PUTNAM EXAM CHALLENGE A coast artillery gun can...Ch. 11.2 - CONCEPT CHECK Describing Coordinates A point in...Ch. 11.2 - Coordinates in SpaceWhat is the y-coordinate of...Ch. 11.2 - CONCEPT CHECK Comparing Graphs Describe the graph...Ch. 11.2 - Parallel Vectors Explain how to determine whether...Ch. 11.2 - Plotting Points In Exercises 5-8. plot the points...Ch. 11.2 - Plotting Points In Exercises 5-8. plot the points...Ch. 11.2 - Plotting Points In Exercises 5-8. plot the points...Ch. 11.2 - Plotting Points In Exercises 5-8. plot the points...Ch. 11.2 - Finding Coordinates of a Point In Exercises 9-12,...Ch. 11.2 - Finding Coordinates of a PointIn Exercises 912,...Ch. 11.2 - Finding Coordinates of a PointIn Exercises 912,...Ch. 11.2 - Finding Coordinates of a PointIn Exercises 912,...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate SystemIn...Ch. 11.2 - Finding the Distance Between Two Points in Space...Ch. 11.2 - Finding the Distance Between Two Points in Space...Ch. 11.2 - Finding the Distance Between Two Points in Space...Ch. 11.2 - Finding the Distance Between Two Points in Space...Ch. 11.2 - Classifying a TriangleIn Exercises 2932, find the...Ch. 11.2 - Classifying a TriangleIn Exercises 2932, find the...Ch. 11.2 - Classifying a TriangleIn Exercises 2932, find the...Ch. 11.2 - Classifying a TriangleIn Exercises 2932, find the...Ch. 11.2 - Finding the Midpoint In Exercises 33-36, find the...Ch. 11.2 - Finding the Midpoint In Exercises 33-36, find the...Ch. 11.2 - Finding the Midpoint In Exercises 33-36, find the...Ch. 11.2 - Finding the Midpoint In Exercises 33-36, find the...Ch. 11.2 - Finding the Equation of a Sphere In Exercises...Ch. 11.2 - Finding the Equation of a SphereIn Exercises 3742,...Ch. 11.2 - Finding the Equation of a SphereIn Exercises 3742,...Ch. 11.2 - Finding the Equation of a SphereIn Exercises 3742,...Ch. 11.2 - Finding the Equation of a SphereIn Exercises 3742,...Ch. 11.2 - Finding the Equation of a SphereIn Exercises 3742,...Ch. 11.2 - Finding the Equation of a SphereIn Exercises 4346,...Ch. 11.2 - Finding the Equation of a SphereIn Exercises 4346,...Ch. 11.2 - Finding the Equation of a SphereIn Exercises 4346,...Ch. 11.2 - Finding the Equation of a Sphere In Exercises...Ch. 11.2 - Finding the Component Form of a Vector in Space In...Ch. 11.2 - Finding the Component Form of a Vector in Space In...Ch. 11.2 - Writing a Vector in Different Forms In Exercises...Ch. 11.2 - Writing a Vector in Different Forms In Exercises...Ch. 11.2 - Finding the Component Form of a Vector in SpaceIn...Ch. 11.2 - Finding the Component Form of a Vector in SpaceIn...Ch. 11.2 - Finding the Component Form of a Vector in SpaceIn...Ch. 11.2 - Finding the Component Form of a Vector in SpaceIn...Ch. 11.2 - Finding a Terminal Point In Exercises 55 and 56,...Ch. 11.2 - Finding a Terminal PointIn Exercises 55 and 56,...Ch. 11.2 - Finding Scalar Multiples In Exercises 57 and 58....Ch. 11.2 - Finding Scalar Multiples In Exercises 57 and 58....Ch. 11.2 - Finding a VectorIn Exercises 5962, find the vector...Ch. 11.2 - Finding a Vector In Exercises 59-62, rind the...Ch. 11.2 - Finding a Vector In Exercises 59-62, rind the...Ch. 11.2 - Finding a Vector In Exercises 59-62, rind the...Ch. 11.2 - Parallel Vectors In Exercises 63-66, determine...Ch. 11.2 - Parallel Vectors In Exercises 63-66, determine...Ch. 11.2 - Parallel Vectors In Exercises 63-66, determine...Ch. 11.2 - Parallel Vectors In Exercises 63-66, determine...Ch. 11.2 - Using Vectors to Determine Collinear Points In...Ch. 11.2 - Using Vectors to Determine Collinear Points In...Ch. 11.2 - Using Vectors to Determine Collinear Points In...Ch. 11.2 - Using Vectors to Determine Collinear Points In...Ch. 11.2 - Verifying a Parallelogram In Exercises 71 and 72,...Ch. 11.2 - Verifying a Parallelogram In Exercises 71 and 72,...Ch. 11.2 - Finding the Magnitude In Exercises 73-78, Find the...Ch. 11.2 - Finding the Magnitude In Exercises 73-78, Find the...Ch. 11.2 - Finding the Magnitude In Exercises 73-78, Find the...Ch. 11.2 - Finding the Magnitude In Exercises 73-78, Find the...Ch. 11.2 - Finding the Magnitude In Exercises 73-78, Find the...Ch. 11.2 - Finding the Magnitude In Exercises 73-78, Find the...Ch. 11.2 - Finding Unit Vectors In Exercises 79-82, find a...Ch. 11.2 - Finding Unit Vectors In Exercises 79-82, find a...Ch. 11.2 - Finding Unit Vectors In Exercises 79-82, find a...Ch. 11.2 - Finding Unit Vectors In Exercises 79-82, find a...Ch. 11.2 - Finding a Vector In Exercises 83-86, find the...Ch. 11.2 - Finding a Vector In Exercises 83-86, find the...Ch. 11.2 - Finding a Vector In Exercises 83-86, And the...Ch. 11.2 - Finding a Vector In Exercises 83-86, And the...Ch. 11.2 - Sketching a Vector In Exercises 87 und 88, sketch...Ch. 11.2 - Sketching a Vector In Exercises 87 und 88, sketch...Ch. 11.2 - Finding a Point Using Vectors In Exercises 89 and...Ch. 11.2 - Finding a Point Using Vectors In Exercises 89 and...Ch. 11.2 - EXPLORING CONCEPTS Writing The initial and...Ch. 11.2 - Writing Let r=(x,y,z) and r0= 1,1,1 . Describe the...Ch. 11.2 - Writing Let r=x,y,z Describe the set of all points...Ch. 11.2 - HOW DO YOU SEE IT? Determine (x, y, z) for each...Ch. 11.2 - Using Vectors (Consider two nonzero vectors u and...Ch. 11.2 - Using Vectors Let u=i+j,v=j+k, and w=an+bv (a)...Ch. 11.2 - Diagonal of a Cube Find the component form of the...Ch. 11.2 - Tower Guy Wire The guy wire supporting a 100-foot...Ch. 11.2 - Auditorium Lights The lights in an auditorium are...Ch. 11.2 - Think About It Suppose the length of each cable in...Ch. 11.2 - Load Supports Find the tension in each of the...Ch. 11.2 - Construction A precast concrete wall is...Ch. 11.2 - GeometryWrite an equation whose graph consists of...Ch. 11.3 - CONCEPT CHECK Dot Product What can you say about...Ch. 11.3 - Direction Cosines Consider the vector v=v1,v2,v3....Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Alternative Form of Dot Product In Exercises 19...Ch. 11.3 - Alternative Form of Dot Product In Exercises 19...Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Classifying a TriangleIn Exercises 2730, the...Ch. 11.3 - Classifying a TriangleIn Exercises 2730, the...Ch. 11.3 - Classifying a TriangleIn Exercises 2730, the...Ch. 11.3 - Classifying a TriangleIn Exercises 2730, the...Ch. 11.3 - Finding Direction AnglesIn Exercises 3136, find...Ch. 11.3 - Finding Direction AnglesIn Exercises 3136, find...Ch. 11.3 - Finding Direction AnglesIn Exercises 3136, find...Ch. 11.3 - Finding Direction AnglesIn Exercises 3136, find...Ch. 11.3 - Finding Direction AnglesIn Exercises 3136, find...Ch. 11.3 - Finding Direction AnglesIn Exercises 3136, find...Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Using Vectors Explain why u+vw is not defined,...Ch. 11.3 - Projection What can be said about the vectors u...Ch. 11.3 - Projection When the projection of u onto v has the...Ch. 11.3 - HOW DO YOU SEE IT? What is known about , the angle...Ch. 11.3 - Revenue The vector u= 3240,1450,2235 gives the...Ch. 11.3 - RevenueRepeat Exercises 49 after decreasing the...Ch. 11.3 - Orthogonal Vectors In Exercises 51-54, find two...Ch. 11.3 - Orthogonal Vectors In Exercises 51-54, find two...Ch. 11.3 - Orthogonal Vectors In Exercises 5154, find two...Ch. 11.3 - Orthogonal Vectors In Exercises 5154, find two...Ch. 11.3 - Finding an Angle Find the angle between a cubes...Ch. 11.3 - Finding an Angle Find the angle between the...Ch. 11.3 - Braking Load A 48,000-pound truck is parked on a...Ch. 11.3 - Braking LoadA 5400-pound sport utility vehicle is...Ch. 11.3 - Work An object is pulled 10 feet across a floor...Ch. 11.3 - WorkA wagon is pulled by exerting a force of 65...Ch. 11.3 - Work A car is towed using a force of 1600 newtons....Ch. 11.3 - Work A pallet truck is pulled by exerting a force...Ch. 11.3 - True or False? In Exercises 63 and 64, determine...Ch. 11.3 - True or False? In Exercises 63 and 64, determine...Ch. 11.3 - Using Points of Intersection In Exercises 6568,...Ch. 11.3 - Using Points of Intersection In Exercises 6568,...Ch. 11.3 - Using Points of Intersection In Exercises 6568,...Ch. 11.3 - Using Points of Intersection In Exercises 6568,...Ch. 11.3 - Proof Use vectors to prove that the diagonals of a...Ch. 11.3 - Proof Use vectors to prove that a parallelogram is...Ch. 11.3 - Bond AngleConsider a regular tetrahedron with...Ch. 11.3 - Proof Consider the vectors u= cos,sin,0 and v=...Ch. 11.3 - Proof Prove the triangle inequality u+v u + v .Ch. 11.3 - Proof Prove theorem 11.6.Ch. 11.3 - Proof Prove the Cauchy-Schwarz Inequality, uv u v...Ch. 11.4 - CONCEPT CHECK Vectors Explain what uv represents...Ch. 11.4 - CONCEPT CHECK Area Explain how to find the area of...Ch. 11.4 - Cross Product of Unit Vectors In Exercises 3-6,...Ch. 11.4 - Cross Product of Unit VectorsIn Exercises 36, find...Ch. 11.4 - Cross Product of Unit Vectors In Exercises 3-6,...Ch. 11.4 - Cross Product of Unit VectorsIn Exercises 36, find...Ch. 11.4 - Finding Cross Products in Exercises 7-10, find (a)...Ch. 11.4 - Finding Cross Products in Exercises 7-10, find (a)...Ch. 11.4 - Finding Cross Products in Exercises 7-10, find (a)...Ch. 11.4 - Finding Cross Products in Exercises 7-10, find (a)...Ch. 11.4 - Finding a Cross Product In Exercises 11-14, find...Ch. 11.4 - Finding a Cross Product In Exercises 11-14, find...Ch. 11.4 - Finding a Cross ProductIn Exercises 1114, find uv...Ch. 11.4 - Finding a Cross Product In Exercises 11-14, find...Ch. 11.4 - Finding a Unit Vector In Exercises 15-18, find a...Ch. 11.4 - Finding a Unit Vector In Exercises 15-18, find a...Ch. 11.4 - Finding a Unit Vector In Exercises 15-18, find a...Ch. 11.4 - Finding a Unit Vector In Exercises 15-18, find a...Ch. 11.4 - Area In Exercises 19-22, find the area of the...Ch. 11.4 - Area In Exercises 19-22, find the area of the...Ch. 11.4 - AreaIn Exercises 1922, find the area of the...Ch. 11.4 - Area In Exercises 19-22, find the area of the...Ch. 11.4 - Area In Exercises 23 and 24, verify that the...Ch. 11.4 - Area In Exercises 23 and 24, verify that the...Ch. 11.4 - Area In Exercises 25 and 26, find the area of the...Ch. 11.4 - AreaIn Exercises 25 and 26, find the area of the...Ch. 11.4 - Torque The brakes on a bicycle are applied using a...Ch. 11.4 - Torque Both the magnitude and the direction of the...Ch. 11.4 - Optimization A force of 180 pounds acts on the...Ch. 11.4 - Optimization A force of 56 pounds acts on the pipe...Ch. 11.4 - Finding a Triple Scalar Product In Exercises...Ch. 11.4 - Finding a Triple Scalar Product In Exercises...Ch. 11.4 - Finding a Triple Scalar Product In Exercises...Ch. 11.4 - Finding a Triple Scalar Product In Exercises...Ch. 11.4 - Volume In Exercises 35 and 36, use t triple scalar...Ch. 11.4 - Volume In Exercises 35 and 36, use t triple scalar...Ch. 11.4 - Volume In Exercises 37 and 38, find the volume of...Ch. 11.4 - Volume In Exercises 37 and 38, find the volume of...Ch. 11.4 - EXPLORING CONCEPTS Comparing Dot Products Identify...Ch. 11.4 - EXPLORING CONCEPTS Using Dot and Cross Products...Ch. 11.4 - EXPLORING CONCEPTS Cross ProductTwo nonzero...Ch. 11.4 - HOW DO YOU SEE IT? The vertices of a triangle in...Ch. 11.4 - True or False? In Exercises 43-46, determine...Ch. 11.4 - True or False? In Exercises 43-46, determine...Ch. 11.4 - True or False? In Exercises 43-46, determine...Ch. 11.4 - True or False? In Exercises 4346, determine...Ch. 11.4 - Proof In Exercises 47-52, prove the property of...Ch. 11.4 - ProofIn Exercises 4752, prove the poverty of the...Ch. 11.4 - Proof In Exercises 47-52, prove the property of...Ch. 11.4 - ProofIn Exercises 4752, prove the poverty of the...Ch. 11.4 - Proof In Exercises 47-52, prove the property of...Ch. 11.4 - ProofIn Exercises 4752, prove the poverty of the...Ch. 11.4 - Proof Prove that uv=uv if u and v are orthogonal.Ch. 11.4 - Proof Prove that u(vw)=(uw)v(uv)w.Ch. 11.4 - Proof Prove Theorem 11.9.Ch. 11.5 - CONCEPT CHECK Parametric and Symmetric...Ch. 11.5 - CONCEPT CHECK Normal Vector The equation of a...Ch. 11.5 - CONCEPT CHECK PlaneWrite an equation of a plane in...Ch. 11.5 - CONCEPT CHECK Parallel Planes Explain how to find...Ch. 11.5 - Checking Points on a Line In Exercises 5 and 6,...Ch. 11.5 - Checking Points on a Line In Exercises 5 and 6,...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Checking Points in a Plane In Exercises 37 and 38,...Ch. 11.5 - Checking Points in a Plane In Exercises 37 and 38,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - 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Finding the Distance Between Two Parallel PlanesIn...Ch. 11.5 - Finding the Distance Between a Point and a LineIn...Ch. 11.5 - Finding the Distance Between a Point and a LineIn...Ch. 11.5 - Finding the Distance Between a Point and a LineIn...Ch. 11.5 - Finding the Distance Between a Point and a LineIn...Ch. 11.5 - Finding the Distance Between Two Parallel Lines In...Ch. 11.5 - Finding the Distance Between Two Parallel LinesIn...Ch. 11.5 - EXPLORING CONCEPTS PlanesConsider a line and a...Ch. 11.5 - EXPLORING CONCEPTS PlanesHow many planes are...Ch. 11.5 - EXPLORING CONCEPTS Think About ItDo two distinct...Ch. 11.5 - HOW DO YOU SEE IT? Match the general equation with...Ch. 11.5 - Modeling Data Personal consumption expenditures...Ch. 11.5 - Mechanical Design The figure shows a chute at the...Ch. 11.5 - DistanceTwo insects are crawling along different...Ch. 11.5 - Finding an Equation of a SphereFind the standard...Ch. 11.5 - Finding a Point of IntersectionFind the point of...Ch. 11.5 - Finding the Distance Between a Plane and a...Ch. 11.5 - Finding Parametric EquationsFind a set of...Ch. 11.5 - Finding Parametric EquationsFind a set of...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - True or False? In Exercises 113-118, determine...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.6 - CONCEPT CHECK Quadric Surfaces How are quadric...Ch. 11.6 - CONCEPT CHECK Classifying an Equation What does...Ch. 11.6 - CONCEPT CHECK Trace of a Surface What is meant by...Ch. 11.6 - CONCEPT CHECK Think About It Does every...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - EXPLORING CONCEPTS HyperboloidExplain how to...Ch. 11.6 - EXPLORING CONCEPTS EllipsoidIs every trace of an...Ch. 11.6 - EXPLORING CONCEPTS Quadric SurfaceIs there a...Ch. 11.6 - HOW DO YOU SEE IT? 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Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in SpaceIn Exercises 4958,...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in SpaceIn Exercises 4958,...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in SpaceIn Exercises 4958,...Ch. 11 - Sketching a Surface in Space In Exercises describe...Ch. 11 - Sketching a Surface in SpaceIn Exercises 4958,...Ch. 11 - Surface of RevolutionFind an equation for the...Ch. 11 - Surface of RevolutionFind an equation for the...Ch. 11 - Converting Rectangular CoordinatesIn Exercises 61...Ch. 11 - Converting Rectangular CoordinatesIn Exercises 61...Ch. 11 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11 - Spherical-to-Rectangular ConversionIn Exercises 65...Ch. 11 - Spherical-to-Rectangular ConversionIn Exercises 65...Ch. 11 - Converting a Rectangular EquationIn Exercises 67...Ch. 11 - Converting a Rectangular Equation In Exercises 67...Ch. 11 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11 - Cylindrical-to- Rectangular ConversionIn Exercises...Ch. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - ProofUsing vectors, prove the Law of Sines: If a,...Ch. 11 - Using an Equation Consider the function...Ch. 11 - Proof Using vectors, prove that the line segments...Ch. 11 - Proof Using vectors, prove that the diagonals of a...Ch. 11 - Distance (a) Find the shortest distance between...Ch. 11 - Orthogonal Vectors Let P0 be a point in the plane...Ch. 11 - Volume (a) Find the volume of the solid bounded...Ch. 11 - Volume (a) Use the disk method to find the volume...Ch. 11 - ProofProve the following property of the cross...Ch. 11 - Using Parametric Equations Consider the line given...Ch. 11 - Sketching Graphs Sketch the graph of each equation...Ch. 11 - Sketching GraphsSketch the graph of each equation...Ch. 11 - Tetherball A tetherball weighing 1 pound is pulled...Ch. 11 - Towing A loaded barge is being towed by two...Ch. 11 - ProofConsider the vectors u=cos,sin,0 and...Ch. 11 - Latitude-Longitude SystemLos Angeles is located at...Ch. 11 - Distance Between a Point and a PlaneConsider the...Ch. 11 - Distance Between Parallel PlanesShow that the...Ch. 11 - Intersection of PlanesShow that the curve of...

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