Explanation Given: a = 3 i − 3 j + k (1) b = 2 i + 4 j − k (2) Formula: Consider three dimensional vectors a and b as follows. a = a 1 i + a 2 j + a 3 k (3) b = b 1 i + b 2 j + b 3 k (4) Write the expression for scalar projection of b onto a . c o m p a b = a ⋅ b | a | (5) Consider a general expression to find the dot product between two three-dimensional vectors. a ⋅ b = 〈 a 1 , a 2 , a 3 〉 ⋅ 〈 b 1 , b 2 , b 3 〉 a ⋅ b = a 1 b 1 + a 2 b 2 + a 3 b 3 (6) Consider a general expression to find the magnitude of a three dimensional vector that is a = 〈 a 1 , a 2 , a 3 〉 . | a | = a 1 2 + a 2 2 + a 3 2 (7) Write the expression for vector projection of b onto a . p r o j a b = a ⋅ b | a | 2 a (8) Compare equation (1) and (3). a = 〈 3 , − 3 , 1 〉 Compare equation (1) and (3). b = 〈 2 , 4 , − 1 〉 In equation (6), substitute 3 for a 1 , –3 for a 2 , 1 for a 3 , 2 for b 1 , 4 for b 2 and –1 for b 3

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ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

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Chapter 12.3, Problem 43E

To determine

To find: The scalar projection of b onto a and the vector projection of b onto a.

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Chapter 12.3, Problem 42E

Chapter 12.3, Problem 44E

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Chapter 12 Solutions

Calculus, Early Transcendentals

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The scalar projection of b onto a and the vector projection of b onto a .

Solution Summary: The author explains how to find the scalar projection of b onto a, and the vector projection, based on three dimensional vectors.

To find: The scalar projection of b onto a and the vector projection of b onto a.

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Chapter 12 Solutions