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Chapter 10: Q. 27 (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 u and v.

Short Answer

Expert verified

The area of the parallelogram determined by the vectors u and v is 213.

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 u and v.

02

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

The cross product of u脳v

localid="1649437514111" u脳v=detijk21-3401

Now solving the determinant.

localid="1649437505083" role="math" u脳v=((1)(1)鈭�(-3)(0))i+((2)(1)鈭�(-3)(4))j+((2)(0)鈭�(1)(4))ku脳v=(1+0)i+(2+12)j+(0鈭�4)ku脳v=1i+14j-4k

03

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

u脳v=1i+14j-4ku脳v=(1)2+(14)2+(-4)2u脳v=1+196+16u脳v=213

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Most popular questions from this chapter

In Exercises 24-27, find compuv, projuv, and the component of v orthogonal tou.

u=1,2,v=3,5

If u, v and w are three vectors in 鈩�3, which of the following products make sense and which do not?

localid="1649346164463" (a)u路(v路w)(b)u路(v脳w)(c)u脳(v路w)(d)u脳(v脳w)

Find the norm of the vector.v=3,鈭�4

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.

the formal未-M,N-鈭�,, and 狈鈥揗 definitions of the limit statements limx鈫�cf(x)=鈭�,limx鈫�鈭�f(x)=L,andlimx鈫�鈭�f(x)=鈭�, respectively

In Exercises 30鈥�35 compute the indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

role="math" localid="1649434688557" v脳wandw脳v
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