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Chapter 9: Q. 51 (page 622)

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

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

Short Answer

Expert verified

The dot product of the vectors v=i-j;w=i+j+kis 0and the angle between them is 蟺2

Step by step solution

01

Step 1. Given

The vectors:

v=i-j;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=(i-j).(i+j+k)=(1)(1)+(-1)(1)+(0)(1)=1-1=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

cos胃=u.vuv

04

Step 4. Find the length of the vectors.

Now,

v=i-j=12+(-1)2=2

w=i+j+k=12+12+12=3

05

Step 5. find the angle between given vectors

Angle between the vectors is given by,

cos胃=v.wvw=023=0胃=cos-1(0)=蟺2

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