   Chapter 12.4, Problem 1E

Chapter
Section
Textbook Problem

# Find the cross product a × b and verify that it is orthogonal to both a and b.1. a = ⟨2, 3, 0⟩, b = ⟨1, 0, 5⟩

To determine

To find: The cross product between a and b and verify a×b is orthogonal to both a and b.

Explanation

Given:

a=2,3,0 and b=1,0,5 .

Formula:

Consider the general expression to find the cross product of a and b.

a×b=|ijka1a2a3b1b2b3| (1)

Condition to verify a×b is orthogonal to a.

(a×b)a=0

Condition to verify a×b is orthogonal to b.

(a×b)b=0

In equation (1), substitute 2 for a1 , 3 for a2 , 0 for a3 , 1 for b1 , 0 for b2 and 5 for b3 .

a×b=|ijk230105|=|3005|i|2015|j+|2310|k=(150)i(100)j+(03)k=15i10j3k

Thus, the a×b is 15i10j3k_

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