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Chapter 9: Q. 47 (page 630)

In Problems 46鈥�49, find the dot product v路w and the angle between v and w.

v=i-3j,w=-i+j

Short Answer

Expert verified

The dot product v路wis -4 and the angle between v and w is 153掳.

Step by step solution

01

Step 1. Given Information 

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

02

Step 2. Finding the dot product 

To find the dot product, use the formula of the dot product which is v路w=a1a2+b1b2.

So,

v路w=1-1+-31v路w=-1-3v路w=-4

03

Step 3. Finding the angle between v and w 

To find the angle between vectors, we will use the formula cos胃=u路vuv.

We have the dot product but to find the length of a vector we will useu=a2+b2.

So,

cos胃=i-3j路-i+j12+-32-12+12cos胃=-420胃=cos-1-420胃鈮�153掳

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Most popular questions from this chapter

In Problems 13鈥�28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

rsin胃=4

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(6.3,3.8)

Match the graph with the polar equation

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