   Chapter 11.4, Problem 13E

Chapter
Section
Textbook Problem

# Finding a Cross Product In Exercises 11-16, find u × v and show that it is orthogonal to both u and v. u =   〈 2 ,   − 3 ,     1 〉 v   =   〈 1 ,   − 2 ,     1 〉

To determine

To calculate: The cross product u×v for the vectors u=2,3,1 and v=1,2,1.

Explanation

Given:

The cross product to be evaluate is u×v. The vectors u and v are u=2,3,1 and v=1,2,1.

Formula used:

The cross product of two vector a=a1i+a2j+a3j and b=b1i+b2j+b3k is:

a×b=|ijka1a2a3b1b2b3|

If two vectors a=a1i+a2j+a3j and b=b1i+b2j+b3k are orthogonal to each other than their dot product is zero that is,

ab=a1b1+a2b2+a3b3=0

Calculation:

The provided vectors are,

u=2i3j+k, v=i2j+k

The cross product a×b is given by,

a×b=|ijka1a2a3b1b2b3|

Therefore, the cross product of vectors u and v is,

u×v=|i

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