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Chapter 10: Q. 34 (page 824)

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

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 vis 78.

Step by step solution

01

Step 1. Given Information 

The indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

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

u脳v=detijk-31-4205

Now solving the determinant.

role="math" u脳v=((1)(5)鈭�(-4)(0))i+((-3)(5)鈭�(-4)(2))j+((-3)(0)鈭�(1)(2))ku脳v=(5-0)i+(-15+8)j+(0鈭�2)ku脳v=5i-7j-2k

03

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

u脳v=5i-7j-2ku脳v=(5)2+(-7)2+(-2)2u脳v=25+49+4u脳v=78

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Most popular questions from this chapter

Give an example of three vectors in 鈩�3that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.

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

u脳wandw脳u

Suppose that we know the reciprocal rule for limits: If limx鈫�cg(x)=Mexists and is nonzero, then limx鈫�c1g(x)=1MThis limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.

Find vand find the unit vector in the direction of v.

v=3,鈭�4

Find the norm of the vector. v=13,13,-13
See all solutions

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