   Chapter 11.4, Problem 11E

Chapter
Section
Textbook Problem

# Finding a Cross Product In Exercises 11-14, find u   × v and show that it is orthogonal to both u and v. u = 〈 4 , − 1 , 0 〉 v = 〈 − 6 , 3 , 0 〉

To determine

To calculate: The cross product u×v for the vectors u=12,3,0 and v=2,5,0.

Explanation

Given:

The cross product:

u×v

The vectors u and v are u=12,3,0 and v=2,5,0.

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=12i3j, v=2i+5j

The cross product a×b is given by,

a×b=|ijka1a2a3b1b2b3|

Therefore the cross product of vectors u and

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