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Chapter 9: Q. 54 (page 631)

In Problems 53 and 54, decompose v into two vectors, one parallel to w and the other orthogonal to w.

v=2i+3j;w=3i+j

Short Answer

Expert verified

The two vectors arev1=2710i+910jandv2=-710i+2110j.

Step by step solution

01

Step 1. Given Information 

The given vectors arev=2i+3jandw=3i+j.

02

Step 2. Finding the vector parallel to w 

Let v1 be the vector parallel to w.To findv1,we will use formulav1=v路ww2w.

First, find the dot product

v路w=2i+3j路3i+jv路w=6+3v路w=9

Now, let's find w2

w=32+12w=10w2=10

Put all the values in the formula

v1=9103i+jv1=2710i+910j

03

Step 3. Finding the vector orthogonal to w

Let v2be the vector orthogonal to w.To findv2,we will use the formulav2=v-v1.

So,

v2=2i+3j-2710i+910jv2=-710i+2110j

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Most popular questions from this chapter

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

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