   Chapter 11.4, Problem 48E

Chapter
Section
Textbook Problem

# True or False? In Exercises 47-50, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If u and v are vectors in space that are nonzero and nonparallel, then u     ×     v = v     ×     u

To determine

Whether the statement “If u and v are vectors in space that are nonzero and nonparallel, then u×v=v×u” is true or false.

Explanation

If u and v are vectors in space that are nonzero and nonparallel, then the cross product of the vectors represents a vector that is perpendicular to the plane of the vectors u and v and its directions is given by the right hand thumb rule. So, direction of the vector u×v is in the direction of the right hand thumb when the fingers goes from the vector u to v. Similarly, the direction of the vector v×u is in the direction of the right hand thumb when the fingers goes from the vector v to u that is in the opposite direction to the vector u×v with the same magnitude.

Therefore,

u×v=v×u

Hence, the provided statement is false.

Now, let vector u and v are u=2i+3jk and v=i+2j+3k.

Evaluate the cross product u×v. The cross product of two vector a=a1i+a2j+a3j and b=b1i+b2j+b3k is:

a×b=|ijka1a2a3b1b2b3|

Therefore, the cross product u×v for vectors u=2i+3

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