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Chapter 9: Q. 54 (page 622)

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

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

Short Answer

Expert verified

The dot product of the vectors

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

is 3 and the angle between them is74.5鈭�.

Step by step solution

01

Step 1. Given

The vectors:

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

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

03

Step 3. Angle between the vectors.

Ifu andv are two nonzero vectors, the angle胃,0鈮�胃鈮�蟺betweenu andv is determined by the formula,cos胃=u.vuv

04

Step 4. Find the length of the vectors.

Now,

v=2i+2j-k=22+22+(-1)2=9=3
w=i+2j+3k=12+22+32=14

05

Step 5. find the angle between given vectors

Angle between the vectors is given by,

cos胃=v.wvw=3914=3314胃=cos-1(114)鈮�74.5掳

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