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Chapter 10: Q. 28 (page 824)

In Exercises 22鈥�29 compute the indicated quantities when u=(2,1,鈭�3),v=(4,0,1),andw=(鈭�2,6,5)

Find the area of the parallelogram determined by the vectors v and w.

Short Answer

Expert verified

The area of the parallelogram determined by the vectors v and w is1096.

Step by step solution

01

Step 1. Given Information 

In Exercises 22鈥�29 compute the indicated quantities when u=(2,1,鈭�3),v=(4,0,1),andw=(鈭�2,6,5)

We have to find the area of the parallelogram determined by the vectors v and w.

02

Step 2. Before finding area of the parallelogram determined by the vectors v and w we have to finding the cross product of v and w. 

The cross product of v脳w

role="math" localid="1649414070213" v脳w=detijk401-265Nowsolvingthedeterminant.v脳w=((0)(5)鈭�(1)(6))i+((4)(5)鈭�(1)(-2))j+((4)(6)鈭�(0)(-2))kv脳w=(0-6)i+(20+2)j+(24+0)kv脳w=-6i+22j+24k

03

Step 3. The area of the parallelogram determined by v and w is v×w

v脳w=-6i+22j+24kv脳w=(-6)2+(22)2+(24)2v脳w=36+484+576v脳w=1096

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Most popular questions from this chapter

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