   Chapter 12.3, Problem 46E

Chapter
Section
Textbook Problem

# For the vectors in Exercise 40, find ortha b and illustrate by drawing the vectors a, b, proja b, and ortha b.

To determine

To find: orthab and illustrate by drawing the vectors a, b, projab and orthab .

Explanation

Formula:

Write the expression to find the vector orthab .

orthab=bprojab (1)

Write the expression for vector projection of b onto a.

projab=ab|a|2a (2)

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

ab=a1,a2b1,b2

ab=a1b1+a2b2 (3)

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

|a|=a12+a22 (4)

In equation (3), substitute 1 for a1 , 4 for a2 , 2 for b1 and 3 for b2 .

ab=(1)(2)+(4)(3)=2+12=14

In equation (4), substitute 1 for a1 and 4 for a2 .

|a|=(1)2+(4)2=1+16=17

In equation (2), substitute 14 for ab , 17 for |a| and 1,4 for a

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