   Chapter 12.3, Problem 47E

Chapter
Section
Textbook Problem

# If a = ⟨3, 0, −1⟩, find a vector b such that compa b = 2.

To determine

To find: Avector b.

Explanation

Given:

a=3,0,1 and compab=2 .

Formula:

Write the expression for the scalar projection of b onto a.

compab=ab|a| (1)

Consider a general expression to find the dot product between two three-dimensional vectors.

ab=a1,a2,a3b1,b2,b3

ab=a1b1+a2b2+a3b3 (2)

Consider a general expression to find the magnitude of a three dimensional vector that is a=a1,a2,a3 .

|a|=a12+a22+a32 (3)

In equation (3), substitute 3 for a1 , 0 for a2 and –1 for a3 .

|a|=(3)2+(0)2+(1)2=9+0+1=10

In equation (1), substitute 2 for compab and 10 for |a|

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