   Chapter 12, Problem 14RQ

Chapter
Section
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.14. For any vectors u and v in V3, (u + v) × v = u × v.

To determine

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

Explanation

Consider the three three-dimensional vectors such as u=u1,u2,u3 and v=v1,v2,v3 .

Cross product of vectors:

Write the expression for cross product of vectors u and v (u×v) .

u×v=|ijku1u2u3v1v2v3|

u×v=(u2v3v2u3)i(u1v3v1u3)j+(u1v2v1u2)k (1)

Find the sum of vectors u and v (u+v) .

u+v=u1,u2,u3+v1,v2,v3=u1+v1,u2+v2,u3+v3

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

(u+v)×v=|ijku1+v1u2+v2u3+v3v1v2v3|=[((u2+v2)v3v2(u3+v3<

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