   Chapter 12, Problem 20RQ

Chapter
Section
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.20. If u × v = 0, then u = 0 or v = 0.

To determine

Whether the given statement is true or false.

Explanation

Formula:

Consider the two three-dimensional vectors such as a=a1,a2,a3 and b=b1,b2,b3.

Cross product of vectors:

Write the expression for cross product of vectors a and b (a×b).

a×b=|ijka1a2a3b1b2b3|

a×b=(a2b3b2a3)i(a1b3b1a3)j+(a1b2b1a2)k (1)

Here,

a1 and b1 are x-coordinates,

a2 and b2 are y-coordinates, and

a3 and b3 are z-coordinates.

The statement If u×v=0, then u=0 or v=0 is false

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