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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
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.

13. For any vectors u and v in V3, (u × v) · u = 0.

To determine

Whether the statement (u×v)u=0 is true or false.

Explanation

Formula used:

Consider the two three-dimensional vectors such as a=a1,a2,a3 and b=b1,b2,b3.

Cross product of vectors:

Write the expression for cross product of vectors a and b (a×b).

a×b=|ijka1a2a3b1b2b3|

a×b=(a2b3b2a3)i(a1b3b1a3)j+(a1b2b1a2)k (1)

Dot product of vectors:

Write the expression for dot product of vectors a and b (ab).

ab=a1,a2,a3b1,b2,b3

ab=a1b1+a2b2+a3b3 (2)

Consider two vectors as u=u1,u2,u3 and v=v1,v2,v3.

Find the value of u×v by using equation (1)

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Chapter 12 Solutions

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P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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