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Chapter 10: Q 23. (page 812)

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=-5,1,3,v=-3,2,7

Short Answer

Expert verified

The dot product is 38 and the angle iscos-1382170.

Step by step solution

01

Step 1. Given information.

The given pairs of vectors are:

u=-5,1,3andv=-3,2,7

02

Step 2. Find the dot product.

The dot product is:u路v=u1v1+u2v2+u3v3

u=-5,1,3andv=-3,2,7u路v=-5-3+12+37=15+2+21=38

Therefore, the dot product of the given two vectors u=-5,1,3andv=-3,2,7is 38.

03

Step 3. Find the angle between the two vectors.

The formula for the angle between the two vectors is:

cos胃=u路vuvu=-5,1,3andv=-3,2,7u路v=38u=-52+12+3225+1+9=35v=-32+22+729+4+49=62

Then,

cos胃=u路vuvcos胃=383562胃=cos-1382170

Therefore, the angle iscos-1382170.

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