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Chapter 9: Q. 51 (page 631)

In Problems 50鈥�52, determine whether v and w are parallel, orthogonal, or neither.

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

Short Answer

Expert verified

The given vectors are neither parallel nor orthogonal.

Step by step solution

01

Step 1. Given Information 

The given vectors arev=-2i+2jandw=-3i+2j.

02

Step 2. Determining whether v and w are parallel or not 

To determine whether the two vectors are parallel or not, we have to find the angle between them because two vectors v and w are said to be parallel if the angle between them is 0or蟺.

Ley's find the angle

cos胃=v路wvwcos胃=-2i+2j路-3i+2j-22+22-32+22cos胃=10104胃=cos-110104胃鈮�11.3掳

Thus, the given vectors are not parallel because the angle is neitherrole="math" localid="1647001247424" 0nor蟺.

03

Step 3. Determining whether v and w are orthogonal or not 

Two vectors v and w are said to be orthogonal if and only if v路w=0.

Let's find the dot product

v路w=-2i+2j路-3i+2jv路w=6+4v路w=10

Thus, the vectors are not orthogonal.

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Most popular questions from this chapter

In Problems 13鈥�28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

r=2

Write the expression in the standard form a+ib.

3cos80掳+isin80掳3

Identify and graph each polar equation. Verify your graph using a graphing utility.
r=2+4cos胃

In Problems 47鈥�52, find the unit vector in the same direction asv:v=i-jv=i-j

Findzwand zw. Leave the answers in polar form.

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