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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337552516

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BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337552516
Chapter 11.4, Problem 20E
Textbook Problem
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Area In Exercises 19-22, find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer algebra system or a graphing utility to verify your result.

u = i + j + k v = j + k

To determine
Area of parallelogram that has given vectors as adjacent sides

Use graphing utility to verify the result

Explanation of Solution

Given: u=i+j+k and v=j+k

Explanation:

u×v=|ijk111011|=i(1.1(1.1))j(1.1(0.1))+k(1

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Chapter 11 Solutions

Calculus: Early Transcendental Functions
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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 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 - Finding a Terminal Point In Exercises 17 and 18,...Ch. 11.1 - Finding a Terminal Point In Exercises 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 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 - Sketching Scalar Multiples In Exercises 25 and 26,...Ch. 11.1 - Sketching Scalar Multiples In Exercises 25 and 26,...Ch. 11.1 - Using Vector Operations In Exercises27 and 28,...Ch. 11.1 - Using Vector Operations In Exercises27 and 28,...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, And the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, And 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, And the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Using the Triangle Inequality In Exercises 43 and...Ch. 11.1 - Using the Triangle Inequality In Exercises 43 and...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 Vector In Exercises 49-52, 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 Vector In Exercises 49-52, 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 It In Exercises 57...Ch. 11.1 - EXPLORING CONCEPTS Think About It In Exercises 57...Ch. 11.1 - EXPLORING CONCEPTS Think About It In Exercises 57...Ch. 11.1 - HOW DO YOU SEE IT? 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The...Ch. 11.3 - A pallet truck is pulled by exerting a force of...Ch. 11.3 - Determine whether the statement is true or false....Ch. 11.3 - Determine whether the statement is true or false....Ch. 11.3 - In exercise y=x2,y=x1/3 (a) Find all points of...Ch. 11.3 - In exercise y=x3,y=x1/3 (a) Find all points of...Ch. 11.3 - In exercise y=1x2,y=x21 (a) Find all points of...Ch. 11.3 - In exercise (y+1)2=x,y=x31 (a) Find all points of...Ch. 11.3 - Use vectors to prove that diagonals of a rhombus...Ch. 11.3 - Use vectors to prove that parallelogram is a...Ch. 11.3 - Consider a regular tetrahedron with vertices...Ch. 11.3 - Consider the vectors u=cos,sin,0 and v=cos,sin,0...Ch. 11.3 - Prove the triangle inequality |u+v|u+v.Ch. 11.3 - Prove theorem 11.6.Ch. 11.3 - Prove the Cauchy-Schwarz inequality |u.v|uv.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 Vectors In Exercises 3-6,...Ch. 11.4 - Cross Product of Unit Vectors In Exercises 3-6,...Ch. 11.4 - Cross Product of Unit Vectors In Exercises 3-6,...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 Product In Exercises 11-14. find...Ch. 11.4 - Finding a Cross Product In Exercises 11-14, find...Ch. 11.4 - Finding a Unit Vector In Exercises 15-18. 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Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric Equations In Exercises 17-24....Ch. 11.5 - Finding Parametric Equations In Exercises 17-24....Ch. 11.5 - Finding Parametric Equations In Exercises 17-24....Ch. 11.5 - Finding Parametric Equations In Exercises 17-24....Ch. 11.5 - Finding Parametric Equations In Exercises 17-24,...Ch. 11.5 - Finding Parametric Equations In Exercises 17-24....Ch. 11.5 - Finding Parametric Equations In Exercises 17-24,...Ch. 11.5 - Finding Parametric Equations In Exercises 17-24....Ch. 11.5 - Using Parametric and Symmetric Equations In...Ch. 11.5 - Using Parametric and Symmetric Equations In...Ch. 11.5 - Using Parametric and Symmetric Equations In...Ch. 11.5 - Using Parametric and Symmetric Equations In...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 Intersection In Exercises...Ch. 11.5 - Finding a Point of Intersection In Exercises...Ch. 11.5 - Finding a Point of Intersection In Exercises...Ch. 11.5 - Finding a Point of Intersection In Exercises...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 Plane In Exercises39-44,...Ch. 11.5 - Finding an Equation of a Plane In Exercises39-44,...Ch. 11.5 - Finding an Equation of a Plane In Exercises39-44,...Ch. 11.5 - Finding an Equation of a Plane In Exercises39-44,...Ch. 11.5 - Finding an Equation of a Plane In Exercises39-44,...Ch. 11.5 - Finding an Equation of a Plane In Exercises39-44,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56....Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises45-56,...Ch. 11.5 - Finding an Equation of a Plane In Exercises 57-60,...Ch. 11.5 - Finding an Equation of a Plane In Exercises 57-60,...Ch. 11.5 - Finding an Equation of a Plane In Exercises 57-60,...Ch. 11.5 - Finding an Equation of a Plane In Exercises 57-60,...Ch. 11.5 - Parallel Planes In Exercises 61-64, determine...Ch. 11.5 - Parallel Planes In Exercises 61-64, determine...Ch. 11.5 - Parallel Planes In Exercises 61-64, determine...Ch. 11.5 - Parallel Planes In Exercises 61-64, determine...Ch. 11.5 - Intersection of Planes In Exercises 65-68, (a)...Ch. 11.5 - Intersection of Planes In Exercises 65-68, (a)...Ch. 11.5 - Intersection of Planes In Exercises 65-68, (a)...Ch. 11.5 - Intersection of Planes In Exercises 65-68, (a)...Ch. 11.5 - Comparing Planes In Exercises 69-74, determine...Ch. 11.5 - Comparing Planes In Exercises 69-74, determine...Ch. 11.5 - Comparing Planes In Exercises 69-74, determine...Ch. 11.5 - Comparing Planes In Exercises 69-74, determine...Ch. 11.5 - Comparing Planes In Exercises 69-74, determine...Ch. 11.5 - Comparing Planes In Exercises 69-74, determine...Ch. 11.5 - Sketching a Graph of a Plane In Exercises75-82,...Ch. 11.5 - Sketching a Graph of a Plane In Exercises75-82,...Ch. 11.5 - Sketching a Graph of a Plane In Exercises75-82,...Ch. 11.5 - Sketching a Graph of a Plane In Exercises75-82,...Ch. 11.5 - Sketching a Graph of a Plane In Exercises75-82,...Ch. 11.5 - Sketching a Graph of a Plane In Exercises75-82,...Ch. 11.5 - Sketching a Graph of a Plane In Exercises75-82,...Ch. 11.5 - Sketching a Graph of a Plane In Exercises75-82,...Ch. 11.5 - Intersection of a Plane and a Line In Exercises...Ch. 11.5 - Intersection of a Plane and a Line In Exercises...Ch. 11.5 - Intersection of a Plane and a Line In Exercises...Ch. 11.5 - Intersection of a Plane and a Line In Exercises...Ch. 11.5 - Finding the Distance Between a Point and a Plane...Ch. 11.5 - Finding the Distance Between a Point and a Plane...Ch. 11.5 - Finding the Distance Between a Point and a Plane...Ch. 11.5 - Finding the Distance Between a Point and a Plane...Ch. 11.5 - Finding the Distance Between Two Parallel Planes...Ch. 11.5 - Finding the Distance Between Two Parallel Planes...Ch. 11.5 - Finding the Distance Between Two Parallel Planes...Ch. 11.5 - Finding the Distance Between Two Parallel Planes...Ch. 11.5 - Finding the Distance Between a Point and a Line In...Ch. 11.5 - Finding the Distance Between a Point and a Line In...Ch. 11.5 - Finding the Distance Between a Point and a Line In...Ch. 11.5 - Finding the Distance Between a Point and a Line In...Ch. 11.5 - Finding the Distance Between Two Parallel Lines In...Ch. 11.5 - Finding the Distance Between Two Parallel Lines In...Ch. 11.5 - EXPLORING CONCEPTS Planes Consider a line and a...Ch. 11.5 - EXPLORING CONCEPTS Planes How many planes are...Ch. 11.5 - EXPLORING CONCEPTS Think About It Do 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 - Distance Two insects are crawling along different...Ch. 11.5 - Finding an Equation of a Sphere Find the standard...Ch. 11.5 - Finding a Point of Intersection Find the point of...Ch. 11.5 - Finding the Distance Between a Plane and a Line...Ch. 11.5 - Finding Parametric Equations Find a set of...Ch. 11.5 - Finding Parametric Equations Find a set of...Ch. 11.5 - True or False? In Exercises 113-118, determine...Ch. 11.5 - True or False? In Exercises 113-118, determine...Ch. 11.5 - True or False? In Exercises 113-118, determine...Ch. 11.5 - True or False? In Exercises 113-118, determine...Ch. 11.5 - True or False? In Exercises 113-118, determine...Ch. 11.5 - True or False? In Exercises 113-118, 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 Space In Exercises11-14,...Ch. 11.6 - Sketching a Surface in Space In Exercises11-14,...Ch. 11.6 - Sketching a Surface in Space In Exercises11-14,...Ch. 11.6 - Sketching a Surface in Space In Exercises11-14,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - Sketching a Quadric Surface In Exercises15-26,...Ch. 11.6 - EXPLORING CONCEPTS Hyperboloid Explain how to...Ch. 11.6 - EXPLORING CONCEPTS Ellipsoid Is every trace of an...Ch. 11.6 - EXPLORING CONCEPTS Quadric Surface Is there a...Ch. 11.6 - HOW DO YOU SEE IT? The four figures below are...Ch. 11.6 - Finding an Equation for a Surface of Revolution In...Ch. 11.6 - Finding an Equation for a Surface of Revolution In...Ch. 11.6 - Finding an Equation for a Surface of Revolution In...Ch. 11.6 - Finding an Equation for a Surface of Revolution In...Ch. 11.6 - Finding an Equation for a Surface of Revolution In...Ch. 11.6 - Finding an Equation for a Surface of Revolution In...Ch. 11.6 - Finding a Generating Curve In Exercises37-40, find...Ch. 11.6 - Finding a Generating Curve In Exercises37-40, find...Ch. 11.6 - Finding a Generating Curve In Exercises37-40, find...Ch. 11.6 - Finding a Generating Curve In Exercises37-40, find...Ch. 11.6 - Finding the Volume of a Solid In Exercises 41 and...Ch. 11.6 - Finding the Volume of a Solid In Exercises 41 and...Ch. 11.6 - Analyzing a Trace In Exercises 43 and 44, analyze...Ch. 11.6 - Analyzing a Trace In Exercises 43 and 44, analyze...Ch. 11.6 - Finding an Equation of a Surface In Exercises 45...Ch. 11.6 - Finding an Equation of a Surface In Exercises 45...Ch. 11.6 - Geography Because of the forces caused by its...Ch. 11.6 - Machine Design The top of a rubber bushing...Ch. 11.6 - Using a Hyperbolic Paraboloid Determine the...Ch. 11.6 - Intersection of Surfaces Explain why the curve of...Ch. 11.6 - Think About It Three types of classic topological...Ch. 11.7 - CONCEPT CHECK Cylindrical Coordinates Describe the...Ch. 11.7 - CONCEPT CHECK Spherical Coordinates Describe the...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Rectangular-to-Spherical Conversion In...Ch. 11.7 - Rectangular-to-Spherical Conversion In...Ch. 11.7 - Rectangular-to-Spherical Conversion In...Ch. 11.7 - Rectangular-to-Spherical Conversion In...Ch. 11.7 - Rectangular-to-Spherical Conversion In...Ch. 11.7 - Rectangular-to-Spherical Conversion In...Ch. 11.7 - Spherical-to-Rectangular Conversion In...Ch. 11.7 - Spherical-to-Rectangular Conversion In...Ch. 11.7 - Spherical-to-Rectangular Conversion In...Ch. 11.7 - Spherical-to-Rectangular Conversion In...Ch. 11.7 - Spherical-to-Rectangular Conversion In...Ch. 11.7 - Spherical-to-Rectangular Conversion In...Ch. 11.7 - Rectangular-to-Spherical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Spherical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Spherical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Spherical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Spherical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Spherical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Spherical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Spherical Conversion In Exercises...Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Spherical Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Spherical Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Spherical Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Spherical Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Spherical Conversion In Exercises...Ch. 11.7 - Cylindrical-to-Spherical Conversion In Exercises...Ch. 11.7 - Spherical-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Spherical-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Spherical-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Spherical-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Spherical-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Spherical-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Matching In Exercises 71-76, match the equation...Ch. 11.7 - Matching In Exercises 71-76, match the equation...Ch. 11.7 - Matching In Exercises 71-76, match the equation...Ch. 11.7 - Matching In Exercises 71-76, match the equation...Ch. 11.7 - Matching In Exercises 71-76, match the equation...Ch. 11.7 - Matching In Exercises 71-76, match the equation...Ch. 11.7 - Spherical Coordinates Explain why in spherical...Ch. 11.7 - HOW DO YOU SEE IT? Identify the surface graphed...Ch. 11.7 - Converting a Rectangular Equation In...Ch. 11.7 - Converting a Rectangular Equation In...Ch. 11.7 - Converting a Rectangular Equation In...Ch. 11.7 - Converting a Rectangular Equation In...Ch. 11.7 - Converting a Rectangular Equation In...Ch. 11.7 - Converting a Rectangular Equation In...Ch. 11.7 - Converting a Rectangular Equation In...Ch. 11.7 - Converting a Rectangular Equation In...Ch. 11.7 - Sketching a Solid In Exercises 87-90, sketch the...Ch. 11.7 - Sketching a Solid In Exercises 87-90, sketch the...Ch. 11.7 - Sketching a Solid In Exercises 87-90, sketch the...Ch. 11.7 - Sketching a Solid In Exercises 87-90, sketch the...Ch. 11.7 - Sketching a Solid In Exercises 91-94, sketch the...Ch. 11.7 - Sketching a Solid In Exercises 91-94, sketch the...Ch. 11.7 - Sketching a Solid In Exercises 91-94, sketch the...Ch. 11.7 - Sketching a Solid In Exercises 91-94, sketch the...Ch. 11.7 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 11.7 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 11.7 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 11.7 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 11.7 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 11.7 - EXPLORING CONCEPTS Think About It In Exercises...Ch. 11.7 - True or False? In Exercises 101 and 102, determine...Ch. 11.7 - True or False? In Exercises 101 and 102, determine...Ch. 11.7 - Intersection of Surfaces Identify the curve of...Ch. 11.7 - Intersection of Surfaces Identify the curve of...Ch. 11 - Writing Vectors in Different Forms In Exercises 1...Ch. 11 - Writing Vectors in Different Forms In Exercises 1...Ch. 11 - Finding a Vector In Exercises 3 and 4, find the...Ch. 11 - Finding a Vector In Exercises 3 and 4, find the...Ch. 11 - Finding Coordinates of a Point Find the...Ch. 11 - Using the Three-Dimensional Coordinate System...Ch. 11 - Finding the Distance Between Two Points in Space...Ch. 11 - Finding the Distance Between Two Points in Space...Ch. 11 - Finding the Equation of a Sphere In Exercises 9...Ch. 11 - Finding the Equation of a Sphere In Exercises 9...Ch. 11 - Finding the Equation of a Sphere In Exercises 11...Ch. 11 - Finding the Equation of a Sphere In Exercises 11...Ch. 11 - Writing a Vector in Different Forms In Exercises...Ch. 11 - Writing a Vector in Different Forms In Exercises...Ch. 11 - Finding a Vector In Exercises 15 and 16, find the...Ch. 11 - Finding a Vector In Exercises 15 and 16, find the...Ch. 11 - Using Vectors to Determine Collinear Points In...Ch. 11 - Using Vectors to Determine Collinear Points In...Ch. 11 - Finding a Unit Vector Find a unit vector in the...Ch. 11 - Finding a Vector Find the vector v of magnitude 8...Ch. 11 - Finding Dot Products In Exercises 21 and 22, let...Ch. 11 - Finding Dot Products In Exercises 21 and 22, let...Ch. 11 - Finding the Angle Between Two Vectors In...Ch. 11 - Finding the Angle Between Two Vectors In...Ch. 11 - Comparing Vectors In Exercises 25 and 26,...Ch. 11 - Comparing Vectors In Exercises 25 and 26,...Ch. 11 - Finding the Projection of u onto v In Exercises 27...Ch. 11 - Finding the Projection of u onto v In Exercises 27...Ch. 11 - Orthogonal Vectors Find two vectors in opposite...Ch. 11 - Work An object is pulled 8 feet across a floor...Ch. 11 - Finding Cross Products In Exercises 31 and 32,...Ch. 11 - Finding Cross Products In Exercises 31 and 32,...Ch. 11 - Finding a Unit Vector Find a unit vector that is...Ch. 11 - Area Find the area of the parallelogram that has...Ch. 11 - Torque A vertical force of 40 pounds acts on a...Ch. 11 - Volume Use the triple scalar product to find the...Ch. 11 - Finding Parametric and Symmetric Equations In...Ch. 11 - Finding Parametric and Symmetric Equations In...Ch. 11 - Finding Parametric Equations In Exercises 39 and...Ch. 11 - Finding Parametric Equations In Exercises 39 and...Ch. 11 - Finding an Equation of a Plane In Exercises 41-44,...Ch. 11 - Finding an Equation of a Plane In Exercises 41-44,...Ch. 11 - Finding an Equation of a Plane In Exercises 41-44,...Ch. 11 - Finding an Equation of a Plane In Exercises 41-44,...Ch. 11 - Distance Find the distance between the point (1,...Ch. 11 - Distance Find the distance between the point...Ch. 11 - Distance Find the distance between the planes...Ch. 11 - Distance Find the distance between the point...Ch. 11 - 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 Space In Exercises 49-58,...Ch. 11 - 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 Space In Exercises 49-58,...Ch. 11 - 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 Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Surface of Revolution Find an equation for the...Ch. 11 - Surface of Revolution Find an equation for the...Ch. 11 - Converting Rectangular Coordinates In Exercises 61...Ch. 11 - Converting Rectangular Coordinates In Exercises 61...Ch. 11 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - Converting a Rectangular Equation In Exercises 67...Ch. 11 - Converting a Rectangular Equation In Exercises 67...Ch. 11 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - Proof Using 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 - Proof Prove 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 Graphs Sketch 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 - Proof Consider the vectors...Ch. 11 - Latitude-Longitude System Los Angeles is located...Ch. 11 - Distance Between a Point and a Plane Consider the...Ch. 11 - Distance Between Parallel Planes Show that the...Ch. 11 - Intersection of Planes Show that the curve of...

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