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Chapter 9: Q. 52 (page 631)

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

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

Short Answer

Expert verified

The given vectors are orthogonal but not parallel.

Step by step solution

01

Step 1. Given Information 

The given vectors arev=3i-2jandw=4i+6j.

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.

Let's find the angle

cos胃=v路wvwcos胃=3i-2j路4i+6j32+-2242+62cos胃=026cos胃=0胃=cos-10胃=蟺2

Thus, the given vectors are not parallel because the angle is neither0nor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=3i-2j路4i+6jv路w=12-12v路w=0

Thus, the vectors are orthogonal.

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Most popular questions from this chapter

In Problems 39鈥�54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

(6.3,3.8)

sin5蟺4=________.

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

Find zw and zw. Leave the answers in polar form.

z=1-iw=1-3i

Use the vectors in the figure at the right to graph each of the following vectors.

3v+u-2w
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