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Chapter 9: Q. 56 (page 622)

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

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

Short Answer

Expert verified

The dot product of the vectors

v=i+3j+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=i+3j+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=(i+3j+2k).(i-j+k)=(1)(1)+(3)(-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,cos胃=u.vuv

04

Step 4. find the angle between given vectors

Angle between the vectors is given by,

cos胃=v.wvw=0vw=0胃=蟺2

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Most popular questions from this chapter

Find the six complex sixth roots of unity (1) and plot them.

Identify and graph each polar equation. Verify your graph using a graphing utility.

r=2+2cos胃

Findzwand zw. Leave the answers in polar form.

role="math" localid="1646661399572" z=2+2iw=3-i

find the unit vector in the same direction asvv=3i-4j

To test if the graph of a polar equation may be symmetric with respect to the line胃=蟺2,replace 胃by ______.
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