   Chapter 12, Problem 13RQ

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.13. For any vectors u and v in V3, (u × v) · u = 0.

To determine

Whether the statement (u×v)u=0 is true or false.

Explanation

Formula used:

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)

Dot product of vectors:

Write the expression for dot product of vectors a and b (ab).

ab=a1,a2,a3b1,b2,b3

ab=a1b1+a2b2+a3b3 (2)

Consider two vectors as u=u1,u2,u3 and v=v1,v2,v3.

Find the value of u×v by using equation (1)

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