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Math Trigonometry Trigonometry (MindTap Course List)

Using Properties of the Dot Product In Exercises 13 - 22 , use the vectors u = 3 , 3 , v = − 4 , 2 , and w = 3 , − 1 to find the quantity. State whether the result is a vector or a scalar. v ⋅ u − w ⋅ v

Using Properties of the Dot Product In Exercises 13 - 22 , use the vectors u = 3 , 3 , v = − 4 , 2 , and w = 3 , − 1 to find the quantity. State whether the result is a vector or a scalar. v ⋅ u − w ⋅ v

Solution Summary: The author explains that the value of the quantity is 8 and the result is a scalar quantity. If u,v,andw are the vectors in the plane or in

Trigonometry (MindTap Course List)

Trigonometry (MindTap Course List)

10th Edition

ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 3.4, Problem 22E

Using Properties of the Dot Product In Exercises 13 - 22 , use the vectors u = 3 , 3 , v = − 4 , 2 , and w = 3 , − 1 to find the quantity. State whether the result is a vector or a scalar.

v ⋅ u − w ⋅ v

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Chapter 3.4, Problem 21E

Chapter 3.4, Problem 23E

Chapter 3 Solutions

Trigonometry (MindTap Course List)

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Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Using the Law of Sines In Exercises 5-22, use the...Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Using the Law of Sines In Exercises 23-32, use the...Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Using the Law of Sines In Exercises 23–32, use the...Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Finding the Area of a Triangle In Exercises 37-44,...Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Height A tree grows at an angle of 4 from the...Ch. 3.1 - A boat is traveling due east parallel to the...Ch. 3.1 - Environmental Science The bearing from the Pine...Ch. 3.1 - Bridge Design A bridge is built across a small...Ch. 3.1 - Angle of Elevation A 10 -meter utility pole casts...Ch. 3.1 - Flight Path A plane flies 500 kilometers with ab...Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Distance Air traffic controllers continuously...Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - True or False? 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One...Ch. 3.2 - Prob. 56E Ch. 3.2 - Prob. 57E Ch. 3.2 - Prob. 58E Ch. 3.2 - Prob. 59E Ch. 3.2 - Prob. 60E Ch. 3.2 - Prob. 61E Ch. 3.2 - True or False? In Exercises 61 and 62, determine...Ch. 3.2 - Prob. 63E Ch. 3.2 - Prob. 64E Ch. 3.2 - Prob. 65E Ch. 3.2 - HOW DO YOU SEE IT? To solve the triangle, would...Ch. 3.2 - Prob. 67E Ch. 3.3 - Show that u and v in the figure at the right are...Ch. 3.3 - Prob. 2ECP Ch. 3.3 - Prob. 3ECP Ch. 3.3 - Prob. 4ECP Ch. 3.3 - Prob. 5ECP Ch. 3.3 - Prob. 6ECP Ch. 3.3 - Prob. 7ECP Ch. 3.3 - Prob. 8ECP Ch. 3.3 - Prob. 9ECP Ch. 3.3 - Prob. 10ECP Ch. 3.3 - Prob. 11ECP Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.3 - Prob. 17E Ch. 3.3 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 28E Ch. 3.3 - Prob. 29E Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E Ch. 3.3 - Prob. 33E Ch. 3.3 - Prob. 34E Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Finding the Magnitude of a Scalar Multiple In...Ch. 3.3 - Prob. 41E Ch. 3.3 - Finding a Unit Vector In Exercises 4146, find a...Ch. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Prob. 44E Ch. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Finding a Unit Vector In Exercises 41-46, find a...Ch. 3.3 - Prob. 47E Ch. 3.3 - Prob. 48E Ch. 3.3 - Prob. 49E Ch. 3.3 - Prob. 50E Ch. 3.3 - Writing a Linear Combination of Unit Vectors In...Ch. 3.3 - Prob. 52E Ch. 3.3 - Prob. 53E Ch. 3.3 - Prob. 54E Ch. 3.3 - Prob. 55E Ch. 3.3 - Prob. 56E Ch. 3.3 - Prob. 57E Ch. 3.3 - Prob. 58E Ch. 3.3 - Prob. 59E Ch. 3.3 - Prob. 60E Ch. 3.3 - Prob. 61E Ch. 3.3 - Prob. 62E Ch. 3.3 - Prob. 63E Ch. 3.3 - Prob. 64E Ch. 3.3 - Prob. 65E Ch. 3.3 - Prob. 66E Ch. 3.3 - Prob. 67E Ch. 3.3 - Prob. 68E Ch. 3.3 - Prob. 69E Ch. 3.3 - Prob. 70E Ch. 3.3 - Prob. 71E Ch. 3.3 - Prob. 72E Ch. 3.3 - Using the Law of Cosines In Exercises 73 and 74,...Ch. 3.3 - Prob. 74E Ch. 3.3 - Prob. 75E Ch. 3.3 - Prob. 76E Ch. 3.3 - Prob. 77E Ch. 3.3 - Velocity Pitcher Aroldis Chapman threw a pitch...Ch. 3.3 - Prob. 79E Ch. 3.3 - Prob. 80E Ch. 3.3 - Prob. 81E Ch. 3.3 - Prob. 82E Ch. 3.3 - Cable Tension The cranes shown in the figure are...Ch. 3.3 - Prob. 84E Ch. 3.3 - Prob. 85E Ch. 3.3 - Physics Use the figure to determine the tension...Ch. 3.3 - Prob. 87E Ch. 3.3 - Prob. 88E Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Inclined Ramp In Exercises 8992, a force of F...Ch. 3.3 - Air Navigation An airplane travels in the...Ch. 3.3 - Prob. 94E Ch. 3.3 - Prob. 95E Ch. 3.3 - True or False? In Exercises 9598, determine...Ch. 3.3 - True or False? In Exercises 9598, determine...Ch. 3.3 - Prob. 98E Ch. 3.3 - Error Analysis Describe the error in finding the...Ch. 3.3 - Prob. 100E Ch. 3.3 - Prob. 101E Ch. 3.3 - Technology Write a program for your graphing...Ch. 3.3 - Finding the Difference of Two Vectors In Exercises...Ch. 3.3 - Finding the Difference of Two Vectors In Exercises...Ch. 3.3 - Graphical Reasoning Consider two forces...Ch. 3.3 - Prob. 106E Ch. 3.3 - Prob. 107E Ch. 3.3 - Prob. 108E Ch. 3.4 - Find each dot product. a. 3,42,3 b. 3,51,8 c....Ch. 3.4 - Prob. 2ECP Ch. 3.4 - Find the angle between u=2,1 and v=1,3.Ch. 3.4 - Prob. 4ECP Ch. 3.4 - Prob. 5ECP Ch. 3.4 - Prob. 6ECP Ch. 3.4 - Prob. 7ECP Ch. 3.4 - Prob. 1E Ch. 3.4 - Vocabulary: Fill in the blanks. The dot product of...Ch. 3.4 - Prob. 3E Ch. 3.4 - Fill in the blanks. The vectors u and v are if...Ch. 3.4 - Fill in the blanks. The projection of u onto v is...Ch. 3.4 - Fill in the blanks. The work W done by a constant...Ch. 3.4 - Prob. 7E Ch. 3.4 - Prob. 8E Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Using Properties of the Dot Product In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Magnitude of a Vector In Exercises...Ch. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Finding the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Using the Angle Between Two Vectors In Exercises...Ch. 3.4 - Prob. 48E Ch. 3.4 - Prob. 49E Ch. 3.4 - Prob. 50E Ch. 3.4 - Prob. 51E Ch. 3.4 - Prob. 52E Ch. 3.4 - Prob. 53E Ch. 3.4 - Prob. 54E Ch. 3.4 - Prob. 55E Ch. 3.4 - Prob. 56E Ch. 3.4 - Decomposing a Vector into Components In Exercises...Ch. 3.4 - Decomposing a Vector into Components In Exercises...Ch. 3.4 - Prob. 59E Ch. 3.4 - Prob. 60E Ch. 3.4 - Finding the Projection of u onto v In Exercises...Ch. 3.4 - Prob. 62E Ch. 3.4 - Prob. 63E Ch. 3.4 - Prob. 64E Ch. 3.4 - Prob. 65E Ch. 3.4 - Prob. 66E Ch. 3.4 - Prob. 67E Ch. 3.4 - Prob. 68E Ch. 3.4 - Prob. 69E Ch. 3.4 - Prob. 70E Ch. 3.4 - Business The vector u=1225,2445 gives the numbers...Ch. 3.4 - Prob. 72E Ch. 3.4 - Prob. 73E Ch. 3.4 - Prob. 74E Ch. 3.4 - Prob. 75E Ch. 3.4 - Work Determine the work done by a crane lifting a...Ch. 3.4 - Prob. 77E Ch. 3.4 - Prob. 78E Ch. 3.4 - Prob. 79E Ch. 3.4 - Prob. 80E Ch. 3.4 - Prob. 81E Ch. 3.4 - Prob. 82E Ch. 3.4 - Prob. 83E Ch. 3.4 - True or False? 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