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Chapter 9: Q. 53 (page 622)

In Problems 51鈥�58, find the dot product v.w and the angle between v and w.

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

Short Answer

Expert verified

The dot product of the vectors v=2i+j-3k;w=i+2j+2k
is -2and the angle between them is 100.3掳

Step by step solution

01

Step 1. Given

The vectors:

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

To find the dot product and the angle between them.

02

Step 2. Dot product of the vectors.

The dot product is given by,

v.w=(2i+j-3k).(i+2j+2k)=(2)(1)+(1)(2)+(-3)(2)=-2

03

Step 3. Angle between the vectors.

If u and v are two nonzero vectors, the angle 胃,0鈮�胃鈮�蟺, between u and v is determined by the formula,

cos胃=u.vuv

04

Step 4. Find the length of the vectors.

Now,

v=2i+j-3k=22+12+(-3)2=14

w=i+2j+2k=12+22+22=9

05

Step 5. find the angle between given vectors

Angle between the vectors is given by,

cos胃=v.wvw=-2149=-2314胃=cos-1(-2314)鈮�100.3掳

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Most popular questions from this chapter

In Problems 39鈥�54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

-3.1,182掳

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=3cos4胃

If the rectangular coordinates of a point are 4,-6,the point symmetric to it with respect to the origin is ______.

In Problems 61鈥�66, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph.

r=3;r=2+2cos胃

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=4cos3胃
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