   Chapter 12.4, Problem 7E

Chapter
Section
Textbook Problem

# Find the cross product a × b and verify that it is orthogonal to both a and b.7. a = ⟨t, 1, 1/t⟩, b = ⟨t2, t2, 1⟩

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=t,1,1t and b=t2,t2,1 .

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 t for a1 , cost for a2 , sint for a3 , 1 for b1 , sint for b2 and cost for b3 .

a×b=|ijkt11tt2t21|=|11tt21|i|t1tt21|j+|t1t2t2|k=(1t)i(tt)j+(t3t2)k=(1t)i+(t3t2)k

Thus, the a×b is (1t)i+(t3t2)k_ .

Find (a×b)a .

Substitute (1t)i+(t3t2)k for a×b and t,1,1t for a

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