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Chapter 9: Q. 50 (page 631)

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

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

Short Answer

Expert verified

The given vectors are parallel but not orthogonal.

Step by step solution

01

Step 1. Given Information

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

So,

cos胃=v路wvwcos胃=2i+3j路-4i-6j22+32-42+-62cos胃=-2626胃=cos-1-1胃=蟺

Thus,vand ware parallel.

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.

So,

v路w=2i+3j路-4i-6jv路w=-8-18v路w=-26

Thus, the vectors are not orthogonal.

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