   Chapter 11.4, Problem 16E

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 = i + 6 j v = − 2 i + j + k

To determine

To calculate: The cross product u×v where; u=i+6j and v=2i+j+k. And to verify that the vector u×v is orthogonal to both the vectors u and v.

Explanation

Given:

The vectors, u and v are given as;

u=i+6jv=2i+j+k

Formula used:

Let, a=a1,a2,a3 and b=b1,b2,b3

Then, the cross product is;

a×b=|ijka1a2a3b1b2b3|=a2b3a3b2,a3b1a1b3,a1b2a2b1

If vectors a and b are perpendicular, then ab=0.

Calculation:

The cross product of vectors u=i+6j and v=2i+j+k is;

u×v=|ijk160211|=i(60)

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