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Chapter 10: Q 20. (page 812)

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

u=1,2,v=3,5

Short Answer

Expert verified

The dot product is 13 and the angle is4.439掳.

Step by step solution

01

Step 1. Given information.

The given pairs of vectors are:

u=1,2,v=3,5

02

Step 2. Find the dot product.

The dot product is: u路v=u1v1+u2v2

u=1,2,v=3,5u路v=13+25=3+10=13

Therefore, the dot product of the given two vectorsu=1,2,v=3,5is 13.

03

Step 3. Find the angle between the two vectors.

The formula for the angle 胃between the two vectors is:

cos胃=u路vuv

u=1,2andv=3,5u路v=13u=12+22=1+4=5v=32+52=9+25=34

Then,

cos胃=u路vuv=13534=13170胃=cos-113170=4.439掳

Therefore, the angle is4.439掳.

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