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Math Calculus Calculus

Finding a Vector In Exercises 73 and 74, find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x -axis. ‖ u ‖ = 1 , θ = 45 ∘ ‖ u + v ‖ = 2 , θ = 90 ∘

Finding a Vector In Exercises 73 and 74, find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x -axis. ‖ u ‖ = 1 , θ = 45 ∘ ‖ u + v ‖ = 2 , θ = 90 ∘

Solution Summary: The author explains the required component form of the vector v, which is langle -1sqrt2.

Calculus

10th Edition

ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Textbook Question

Chapter 11.1, Problem 73E

Finding a Vector In Exercises 73 and 74, find the component form of v given the magnitudes of u and u + v

and the angles that u and u + v

make with the positive x-axis.

‖ u ‖ = 1 , θ = 45 ∘ ‖ u + v ‖ = 2 , θ = 90 ∘

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Chapter 11.1, Problem 72E

Chapter 11.1, Problem 74E

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Chapter 11 Solutions

Calculus

Ch. 11.1 - CONCEPT CHECK Scalar and Vector Describe the...Ch. 11.1 - Sketching a Vector In Exercises 3 and 4, (a) find...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E

Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Sketching Scalar MultipliesIn Exercises 25 and 26,...Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Finding MagnitudesIn Exercises 3942, find the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.1 - Prob. 47E Ch. 11.1 - Prob. 48E Ch. 11.1 - Prob. 49E Ch. 11.1 - Prob. 50E Ch. 11.1 - Prob. 51E Ch. 11.1 - Prob. 52E Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Prob. 54E Ch. 11.1 - Prob. 55E Ch. 11.1 - Prob. 56E Ch. 11.1 - Prob. 58E Ch. 11.1 - Prob. 59E Ch. 11.1 - Prob. 60E Ch. 11.1 - Prob. 61E Ch. 11.1 - Prob. 62E Ch. 11.1 - Prob. 63E Ch. 11.1 - Prob. 64E Ch. 11.1 - Prob. 65E Ch. 11.1 - Prob. 66E Ch. 11.1 - Prob. 67E Ch. 11.1 - Prob. 68E Ch. 11.1 - Prob. 69E Ch. 11.1 - Prob. 70E Ch. 11.1 - Finding Unit Vectors In Exercises 67-72, find a...Ch. 11.1 - Prob. 72E Ch. 11.1 - Finding a Vector In Exercises 73 and 74, find the...Ch. 11.1 - Prob. 74E Ch. 11.1 - Prob. 75E Ch. 11.1 - Numerical and Graphical Analysis Forces with...Ch. 11.1 - Prob. 77E Ch. 11.1 - Prob. 78E Ch. 11.1 - Prob. 79E 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 - Prob. 82E 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 - Prob. 85E Ch. 11.1 - Prob. 86E Ch. 11.1 - Prob. 87E Ch. 11.1 - Prob. 88E Ch. 11.1 - Prob. 89E Ch. 11.1 - Prob. 90E Ch. 11.1 - Prob. 91E Ch. 11.1 - Prob. 92E Ch. 11.1 - Prob. 93E Ch. 11.1 - Prob. 94E Ch. 11.1 - Prob. 95E Ch. 11.1 - Prob. 96E Ch. 11.2 - CONCEPT CHECK Describing Coordinates A point in...Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Finding Coordinates of a PointIn Exercises 912,...Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Classifying a TriangleIn Exercises 2932, find the...Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Finding the Midpoint In Exercises 33-36, find the...Ch. 11.2 - Prob. 34E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E 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 - Prob. 45E Ch. 11.2 - Prob. 46E Ch. 11.2 - Prob. 47E Ch. 11.2 - Prob. 48E Ch. 11.2 - Prob. 51E Ch. 11.2 - Prob. 52E Ch. 11.2 - Finding the Component Form of a Vector in SpaceIn...Ch. 11.2 - Prob. 53E Ch. 11.2 - Prob. 54E Ch. 11.2 - Prob. 55E Ch. 11.2 - Prob. 56E Ch. 11.2 - Prob. 57E Ch. 11.2 - Prob. 58E Ch. 11.2 - Prob. 59E Ch. 11.2 - Prob. 60E Ch. 11.2 - Prob. 61E Ch. 11.2 - Prob. 62E Ch. 11.2 - Prob. 63E Ch. 11.2 - Prob. 64E Ch. 11.2 - Prob. 65E Ch. 11.2 - Prob. 66E Ch. 11.2 - Prob. 67E Ch. 11.2 - Prob. 68E Ch. 11.2 - Prob. 69E Ch. 11.2 - Prob. 70E Ch. 11.2 - Prob. 71E Ch. 11.2 - Prob. 72E Ch. 11.2 - Prob. 73E Ch. 11.2 - Prob. 74E Ch. 11.2 - Prob. 75E Ch. 11.2 - Prob. 76E Ch. 11.2 - Prob. 77E Ch. 11.2 - Prob. 78E Ch. 11.2 - Prob. 79E Ch. 11.2 - Prob. 80E Ch. 11.2 - Prob. 81E Ch. 11.2 - Prob. 82E Ch. 11.2 - Prob. 83E Ch. 11.2 - Prob. 84E Ch. 11.2 - Prob. 85E Ch. 11.2 - Prob. 86E Ch. 11.2 - Prob. 87E Ch. 11.2 - Sketching a Vector In Exercises 87 und 88, sketch...Ch. 11.2 - Prob. 89E Ch. 11.2 - Prob. 90E Ch. 11.2 - Prob. 92E Ch. 11.2 - Prob. 91E Ch. 11.2 - Prob. 94E Ch. 11.2 - Prob. 95E Ch. 11.2 - Prob. 96E Ch. 11.2 - Prob. 97E Ch. 11.2 - Prob. 98E Ch. 11.2 - Prob. 99E Ch. 11.2 - Prob. 100E Ch. 11.2 - Auditorium Lights The lights in an auditorium are...Ch. 11.2 - Prob. 102E Ch. 11.2 - Load Supports Find the tension in each of the...Ch. 11.2 - Prob. 104E Ch. 11.2 - Prob. 105E Ch. 11.3 - Finding Dot ProductsIn Exercises 310, find (a) uv...Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E 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 - Prob. 12E 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 - Prob. 15E Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Comparing VectorsIn Exercises 2126, determine...Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Prob. 37E Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Prob. 42E Ch. 11.3 - Prob. 43E Ch. 11.3 - Prob. 44E Ch. 11.3 - Prob. 45E Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.3 - Projection When the projection of u onto v has the...Ch. 11.3 - Prob. 50E Ch. 11.3 - Revenue The vector u= 3240,1450,2235 gives the...Ch. 11.3 - RevenueRepeat Exercises 49 after decreasing the...Ch. 11.3 - Prob. 53E Ch. 11.3 - Prob. 54E Ch. 11.3 - Prob. 55E Ch. 11.3 - Prob. 56E Ch. 11.3 - Prob. 57E Ch. 11.3 - Prob. 58E Ch. 11.3 - Prob. 59E Ch. 11.3 - Prob. 60E Ch. 11.3 - Prob. 61E Ch. 11.3 - Prob. 62E Ch. 11.3 - Prob. 63E Ch. 11.3 - Prob. 64E Ch. 11.3 - Prob. 65E Ch. 11.3 - Prob. 66E Ch. 11.3 - Prob. 67E Ch. 11.3 - Prob. 68E Ch. 11.3 - Prob. 69E Ch. 11.3 - Prob. 70E 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 - Prob. 74E Ch. 11.3 - Prob. 75E Ch. 11.3 - Proof Prove the Cauchy-Schwarz Inequality, uv u v...Ch. 11.3 - Prob. 77E Ch. 11.3 - Prob. 78E Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Prob. 3E Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Prob. 25E Ch. 11.4 - Area In Exercises 23 and 24, verify that the...Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Torque The brakes on a bicycle are applied using a...Ch. 11.4 - Prob. 30E 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 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E 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 - Prob. 41E Ch. 11.4 - Prob. 42E Ch. 11.4 - Prob. 43E Ch. 11.4 - Prob. 44E Ch. 11.4 - Prob. 45E Ch. 11.4 - Prob. 46E Ch. 11.4 - Prob. 47E Ch. 11.4 - Prob. 48E Ch. 11.4 - Prob. 49E Ch. 11.4 - Prob. 50E Ch. 11.4 - Prob. 51E Ch. 11.4 - Prob. 52E Ch. 11.4 - Prob. 53E Ch. 11.4 - Prob. 54E Ch. 11.4 - Proof In Exercises 47-52, prove the property of...Ch. 11.4 - Prob. 56E Ch. 11.4 - Proof Prove that uv=uv if u and v are orthogonal.Ch. 11.4 - Prob. 58E Ch. 11.4 - Prob. 59E Ch. 11.5 - CONCEPT CHECK Parametric and Symmetric...Ch. 11.5 - Prob. 1E Ch. 11.5 - Prob. 2E Ch. 11.5 - Prob. 3E Ch. 11.5 - Prob. 4E Ch. 11.5 - Prob. 5E Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Prob. 7E Ch. 11.5 - Prob. 8E Ch. 11.5 - Prob. 9E Ch. 11.5 - Prob. 10E Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Prob. 12E Ch. 11.5 - Prob. 13E Ch. 11.5 - Prob. 14E Ch. 11.5 - Prob. 15E Ch. 11.5 - Prob. 16E Ch. 11.5 - Prob. 17E Ch. 11.5 - Prob. 18E Ch. 11.5 - Prob. 19E Ch. 11.5 - Prob. 20E Ch. 11.5 - Prob. 21E Ch. 11.5 - Prob. 22E Ch. 11.5 - Prob. 23E Ch. 11.5 - Prob. 24E Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Prob. 26E Ch. 11.5 - Prob. 27E Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Prob. 30E Ch. 11.5 - Prob. 31E Ch. 11.5 - Prob. 32E Ch. 11.5 - Prob. 33E Ch. 11.5 - Prob. 34E Ch. 11.5 - Prob. 35E 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 - Prob. 38E Ch. 11.5 - Prob. 39E 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 - Prob. 54E Ch. 11.5 - Prob. 55E Ch. 11.5 - Prob. 56E Ch. 11.5 - Prob. 71E Ch. 11.5 - Prob. 72E Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Prob. 74E Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Prob. 76E Ch. 11.5 - Prob. 57E Ch. 11.5 - Prob. 58E Ch. 11.5 - Prob. 59E Ch. 11.5 - Prob. 60E Ch. 11.5 - Prob. 61E Ch. 11.5 - Prob. 62E Ch. 11.5 - Prob. 63E Ch. 11.5 - Prob. 64E Ch. 11.5 - Prob. 65E Ch. 11.5 - Prob. 66E Ch. 11.5 - Prob. 67E Ch. 11.5 - Prob. 68E Ch. 11.5 - Prob. 69E Ch. 11.5 - Prob. 70E Ch. 11.5 - Prob. 77E Ch. 11.5 - Prob. 78E Ch. 11.5 - Prob. 79E Ch. 11.5 - Prob. 80E Ch. 11.5 - Prob. 81E Ch. 11.5 - Prob. 82E Ch. 11.5 - Prob. 83E Ch. 11.5 - Prob. 84E Ch. 11.5 - Prob. 85E Ch. 11.5 - Finding the Distance Between Two Parallel Planes...Ch. 11.5 - Prob. 87E Ch. 11.5 - Prob. 88E Ch. 11.5 - Prob. 89E Ch. 11.5 - Prob. 90E Ch. 11.5 - Prob. 91E Ch. 11.5 - Prob. 92E Ch. 11.5 - Prob. 93E Ch. 11.5 - Prob. 94E Ch. 11.5 - Prob. 96E Ch. 11.5 - Prob. 97E Ch. 11.5 - Prob. 98E Ch. 11.5 - Prob. 99E Ch. 11.5 - HOW DO YOU SEE IT? Match the general equation with...Ch. 11.5 - Prob. 101E Ch. 11.5 - Mechanical Design The figure shows a chute at the...Ch. 11.5 - DistanceTwo insects are crawling along different...Ch. 11.5 - Prob. 104E Ch. 11.5 - Finding a Point of IntersectionFind the point of...Ch. 11.5 - Prob. 106E Ch. 11.5 - Finding a Point of Intersection Find the point of...Ch. 11.5 - Prob. 108E Ch. 11.5 - Prob. 109E Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - Prob. 111E Ch. 11.5 - Prob. 112E Ch. 11.5 - Prob. 113E Ch. 11.5 - Prob. 114E Ch. 11.6 - Prob. 1E Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Prob. 3E Ch. 11.6 - Prob. 4E Ch. 11.6 - Prob. 5E Ch. 11.6 - Prob. 6E Ch. 11.6 - Prob. 7E Ch. 11.6 - Prob. 8E Ch. 11.6 - Prob. 9E Ch. 11.6 - Prob. 10E Ch. 11.6 - Prob. 11E Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Prob. 17E Ch. 11.6 - Prob. 13E Ch. 11.6 - Prob. 14E Ch. 11.6 - Prob. 15E Ch. 11.6 - Prob. 20E Ch. 11.6 - Prob. 16E Ch. 11.6 - Prob. 18E Ch. 11.6 - Prob. 23E Ch. 11.6 - Prob. 19E Ch. 11.6 - Prob. 21E Ch. 11.6 - Prob. 22E Ch. 11.6 - Prob. 24E Ch. 11.6 - Prob. 25E Ch. 11.6 - Prob. 26E Ch. 11.6 - Prob. 27E Ch. 11.6 - Prob. 28E Ch. 11.6 - Prob. 29E Ch. 11.6 - Prob. 36E Ch. 11.6 - Prob. 35E Ch. 11.6 - Prob. 30E Ch. 11.6 - Prob. 31E 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 - Prob. 34E Ch. 11.6 - Finding a Generating CurveIn Exercises 3740, find...Ch. 11.6 - Prob. 38E Ch. 11.6 - Prob. 39E Ch. 11.6 - Prob. 40E Ch. 11.6 - Prob. 41E Ch. 11.6 - Analyzing a TraceIn Exercises 43 and 44, analyze...Ch. 11.6 - Prob. 43E Ch. 11.6 - Prob. 44E Ch. 11.6 - Prob. 45E Ch. 11.6 - Machine Design The top of a rubber bushing...Ch. 11.6 - Using a Hyperbolic ParaboloidDetermine the...Ch. 11.6 - Prob. 48E Ch. 11.6 - Prob. 49E Ch. 11.6 - True or False? In Exercises 49-52, determine...Ch. 11.6 - Prob. 51E Ch. 11.6 - Prob. 52E Ch. 11.6 - Prob. 53E Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Prob. 3E Ch. 11.7 - Prob. 4E Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Prob. 6E Ch. 11.7 - Prob. 7E Ch. 11.7 - Prob. 8E Ch. 11.7 - Prob. 9E Ch. 11.7 - Prob. 10E Ch. 11.7 - Prob. 11E Ch. 11.7 - Prob. 12E Ch. 11.7 - Prob. 13E Ch. 11.7 - Prob. 14E Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Rectangular-to-Cylindrical Conversion In Exercises...Ch. 11.7 - Prob. 17E Ch. 11.7 - Prob. 18E Ch. 11.7 - Prob. 19E Ch. 11.7 - Prob. 20E Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Prob. 22E Ch. 11.7 - Prob. 23E Ch. 11.7 - Prob. 24E Ch. 11.7 - Prob. 25E Ch. 11.7 - Prob. 26E Ch. 11.7 - Prob. 27E Ch. 11.7 - Prob. 28E Ch. 11.7 - Prob. 29E Ch. 11.7 - Rectangular-to-Spherical ConversionIn Exercises...Ch. 11.7 - Prob. 31E Ch. 11.7 - Prob. 32E Ch. 11.7 - Prob. 33E Ch. 11.7 - Prob. 34E Ch. 11.7 - Prob. 35E Ch. 11.7 - Prob. 36E Ch. 11.7 - Prob. 37E Ch. 11.7 - Prob. 38E Ch. 11.7 - Prob. 39E Ch. 11.7 - Prob. 40E Ch. 11.7 - Prob. 41E Ch. 11.7 - Prob. 42E Ch. 11.7 - Prob. 43E Ch. 11.7 - Prob. 44E Ch. 11.7 - Prob. 45E Ch. 11.7 - Prob. 46E Ch. 11.7 - Prob. 47E Ch. 11.7 - Rectangular-to-Spherical ConversionIn Exercises...Ch. 11.7 - Prob. 49E Ch. 11.7 - Prob. 50E Ch. 11.7 - Prob. 51E Ch. 11.7 - Prob. 52E Ch. 11.7 - Prob. 53E Ch. 11.7 - Prob. 54E Ch. 11.7 - Prob. 55E Ch. 11.7 - Prob. 56E Ch. 11.7 - Prob. 63E Ch. 11.7 - Prob. 64E Ch. 11.7 - Prob. 68E Ch. 11.7 - Prob. 69E Ch. 11.7 - Prob. 70E Ch. 11.7 - Prob. 71E Ch. 11.7 - Prob. 72E Ch. 11.7 - Prob. 75E Ch. 11.7 - Prob. 76E Ch. 11.7 - Prob. 77E Ch. 11.7 - Prob. 78E Ch. 11.7 - Prob. 57E Ch. 11.7 - Prob. 58E Ch. 11.7 - Prob. 59E Ch. 11.7 - Prob. 60E Ch. 11.7 - Prob. 61E Ch. 11.7 - Prob. 62E Ch. 11.7 - Spherical Coordinates Explain why in spherical...Ch. 11.7 - Prob. 82E Ch. 11.7 - Prob. 65E Ch. 11.7 - Prob. 66E Ch. 11.7 - Prob. 67E Ch. 11.7 - Prob. 73E Ch. 11.7 - Prob. 74E Ch. 11.7 - Prob. 79E Ch. 11.7 - Prob. 81E Ch. 11.7 - Prob. 83E Ch. 11.7 - Prob. 84E Ch. 11.7 - Prob. 85E Ch. 11.7 - Prob. 86E Ch. 11.7 - Prob. 87E Ch. 11.7 - Prob. 88E Ch. 11.7 - Prob. 89E Ch. 11.7 - Prob. 90E Ch. 11.7 - Prob. 91E Ch. 11.7 - Prob. 92E Ch. 11.7 - Prob. 93E Ch. 11.7 - Prob. 94E Ch. 11.7 - Prob. 95E Ch. 11.7 - Sketching a Solid In Exercises 9194, sketch the...Ch. 11.7 - Prob. 97E Ch. 11.7 - Prob. 98E Ch. 11.7 - Prob. 99E Ch. 11.7 - Prob. 100E Ch. 11.7 - Prob. 101E Ch. 11.7 - Prob. 102E Ch. 11.7 - Prob. 103E Ch. 11.7 - Prob. 104E Ch. 11.7 - Prob. 105E Ch. 11.7 - Prob. 106E Ch. 11.7 - Prob. 107E Ch. 11.7 - Prob. 108E Ch. 11.7 - Intersection of SurfaceIdentify the curve of...Ch. 11.7 - Prob. 110E Ch. 11 - Writing Vectors in Different Forms In Exercises 1...Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Finding a Unit VectorFind a unit vector that is...Ch. 11 - Prob. 38RE Ch. 11 - Prob. 39RE Ch. 11 - VolumeUse the triple scalar product to find the...Ch. 11 - Prob. 41RE Ch. 11 - Prob. 42RE Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Prob. 47RE Ch. 11 - Prob. 48RE Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 51RE Ch. 11 - Prob. 52RE Ch. 11 - Distance Find the distance between the planes...Ch. 11 - Prob. 54RE Ch. 11 - Prob. 55RE Ch. 11 - Prob. 56RE Ch. 11 - Prob. 57RE Ch. 11 - Prob. 58RE Ch. 11 - Prob. 59RE Ch. 11 - Prob. 60RE Ch. 11 - Prob. 61RE Ch. 11 - Prob. 62RE Ch. 11 - Prob. 63RE Ch. 11 - Prob. 64RE Ch. 11 - Prob. 65RE Ch. 11 - Prob. 66RE Ch. 11 - Prob. 67RE Ch. 11 - Prob. 68RE Ch. 11 - Prob. 69RE Ch. 11 - Prob. 70RE Ch. 11 - Prob. 71RE Ch. 11 - Prob. 72RE Ch. 11 - Prob. 73RE Ch. 11 - Prob. 74RE Ch. 11 - Prob. 75RE Ch. 11 - Prob. 76RE Ch. 11 - Prob. 77RE Ch. 11 - Prob. 78RE Ch. 11 - Prob. 1PS Ch. 11 - Prob. 2PS Ch. 11 - Prob. 3PS Ch. 11 - Prob. 4PS Ch. 11 - Prob. 5PS Ch. 11 - Prob. 6PS Ch. 11 - Volume (a) Find the volume of the solid bounded...Ch. 11 - Prob. 8PS Ch. 11 - Prob. 9PS Ch. 11 - Prob. 10PS Ch. 11 - Sketching Graphs Sketch the graph of each equation...Ch. 11 - Prob. 12PS Ch. 11 - Tetherball A tetherball weighing 1 pound is pulled...Ch. 11 - Towing A loaded barge is being towed by two...Ch. 11 - Prob. 15PS Ch. 11 - Latitude-Longitude SystemLos Angeles is located at...Ch. 11 - Distance Between a Point and a PlaneConsider the...Ch. 11 - Prob. 18PS Ch. 11 - Prob. 19PS Ch. 11 - Prob. 20PS

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Finding Lengths, Unit Vectors, and Dot Products In Exercises 29-34, use a software program or a graphing utility to find (a) the lengths of u and v, (b) a unit vector in the direction of v, (c) a unit vector in the direction opposite that of u, (d) uv, (e) uu, and (f) vv. u=(1,18,25), v=(0,14,15)
Finding a Unit Vector In Exercises 41-46, find a unit vector u in the direction of v. Verify that u=1. v=1,6
Fill in the blanks. The vectors u and v are if and only if uv=0.

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