   Chapter 12.4, Problem 3E

Chapter
Section
Textbook Problem

# Find the cross product a × b and verify that it is orthogonal to both a and b.3. a = 2j − 4k, b = −i + 3j + k

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=2j4k and b=i+3j+k .

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 0 for a1 , 2 for a2 , –4 for a3 , –1 for b1 , 3 for b2 and 1 for b3 .

a×b=|ijk024131|=|2431|i|0411|j+|0213|k=(2+12)i(04)j+(0+2)k=14i+4j+2k

Thus, the a×b is 14i+4j+2k_

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