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Chapter 9: Q. 58 (page 622)

In Problems 51鈥�58, find the dot product v.w and the angle between v and w.v=3i-4j+k;w=6i-8j+2k

Short Answer

Expert verified

The dot product of the vectors

v=3i-4j+k;w=6i-8j+2k

is 52 and the angle between them is 0.

Step by step solution

01

Step 1. Given

The vectors:

v=3i-4j+k;w=6i-8j+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=(3i-4j+k).(6i-8j+2k)=(3)(6)+(-4)(-8)+(1)(2)=52

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=3i-4j+k=32+(-4)2+(1)2=26

w=6i-8j+2k=62+(-8)2+22=102

05

Step 5. find the angle between given vectors

Angle between the vectors is given by,

cos胃=v.wvw=5226102=5252胃=cos-1(1)鈮�0

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