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Chapter 9: Q. 55 (page 622)

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

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

Short Answer

Expert verified

The dot product of the vectors

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

is 0 and the angle between them is 蟺2.

Step by step solution

01

Step 1. Given

The vectors:

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

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=(3i-j+2k).(i+j-k)=(3)(1)+(-1)(1)+(2)(-1)=0

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,localid="1646807346417" cos胃=u.vuv

04

Step 4. Find the length of the vectors.

Now,

v=3i-j+2k=32+(-1)2+(2)2=14

w=i+j-k=12+12+(-1)2=3

05

Step 5. find the angle between given vectors

Angle between the vectors is given by,

cos胃=v.wvw=0143=0314胃=cos-1(0314)鈮�蟺2

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