   Chapter 12.4, Problem 22E

Chapter
Section
Textbook Problem

# Show that (a × b) · b = 0 for all vectors a and b in V3.

To determine

To show: The (a×b)b=0 for all vectors a and b in V3 .

Explanation

Consider a=a1,a2,a3 and b=b1,b2,b3 .

Find the cross product between a and b .

a×b=|ijka1a2a3b1b2b3|=|a2a3b2b3|i|a1a3b1b3|j+|a1a2b1b2|k=(a2b3a3b2)i(a1b3a3b1)j+(a1b2a2b1)k

Find (a×b)b

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