   Chapter 12, Problem 22RQ

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.22. If u and v are in V3, then |u · v| ≤ |u| |v|.

To determine

Whetherthe statement |uv||u||v| is true or false.

Explanation

Formula used:

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

ab=|a||b|cosθ (1)

Here,

|a| is magnitude if vector a,

|b| is magnitude of vector b, and

θ is angle between vectors a and b.

Consider the given statement.

|uv||u||v|

Write the expression for dot product of vectors u and v by using equation (1).

uv=|u||v|cosθ

Here,

|u|0 and |v|0

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