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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
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.

If F is a vector field, then curl F is a vector field.

To determine

Whether the statement “If F is a vector field, then Curl F is a vector field” is true or false.

Explanation

Formula used:

Consider the two three-dimensional vectors such as a=a1i+a2j+a3k and  b=b1i+b2j+b3k .

Write the expression of cross product between the three vectors a and b.

a×b=|ijka1a2a3b1b2b3| (1)

Consider F is a three-dimensional vector field that is F(x,y,z)=F1i+F2j+F3k .

The CurlF is calculated as follows.

×F=(xi+yj+zk)×(F1i+F2j+F3k)

Find the cross product of these two vectors using equation (1)

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Chapter 16 Solutions

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