   Chapter 12.3, Problem 61E

Chapter
Section
Textbook Problem

# Use Theorem 3 to prove the Cauchy-Schwarz Inequality: | a · b| ≤ | a | | b |

To determine

To prove: The Cauchy-Schwarz Inequality theorem.

Explanation

Formula used:

Write the expression to find ab in terms of θ .

ab=|a||b|cosθ (1)

Here,

|u| is the magnitude of u vector,

|v| is the magnitude of v vector, and

θ is the angle between vectors u and v.

The Cauchy-Schwarz Inequality theorem is defined as follows.

|ab||a||b|

Take the magnitude on both sides in equation (1)

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