   Chapter 12, Problem 8RQ

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.8. For any vectors u and v in V3 and any scalar k, k(u · v) = (ku) · v

To determine

Whether the statement k(uv)=(ku)v is true or false.

Explanation

Formula used:

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

Dot product of vectors:

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

ab=a1,a2,a3b1,b2,b3=a1b1+a2b2+a3b3

Property 4 of dot product:

Write the expression for property 4 of the dot product of vectors.

(ca)b=c(ab) (1)

Here,

c is scalar.

Consider the given statement

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