   Chapter 12.3, Problem 39E

Chapter
Section
Textbook Problem

# Find the scalar and vector projections of b onto a.39. a = ⟨−5, 12⟩, b = ⟨4, 6⟩

To determine

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

Explanation

Given:

a=5,12 and b=4,6

Formula:

Write the expression for scalar projection of b onto a.

compab=ab|a| (1)

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

ab=a1,a2b1,b2

ab=a1b1+a2b2 (2)

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

|a|=a12+a22 (3)

Write the expression for vector projection of b onto a.

projab=ab|a|2a (4)

In equation (2), substitute –5 for a1 , 12 for a2 , 4 for b1 and 6 for b2 .

ab=(5)(4)+(12)(6)=20+72=52

In equation (3), substitute –5 for a1 and 12 for a2

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