Chapter 12.3, Problem 62E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

The Triangle Inequality for vectors is

| **a** + **b** | ≤ | **a** | + | **b** |

(a) Give a geometric interpretation of the Triangle Inequality.

(b) Use the Cauchy-Schwarz Inequality from Exercise 61 to prove the Triangle Inequality. [*Hint*: Use the fact that | **a + b** |^{2} = (**a + b**) **·** (**a + b**) and use Property 3 of the dot product.]

(a)

To determine

**To obtain:** A geometric interpretation of the Triangle Inequality.

Explanation

**Given:**

Triangle Inequality for vectors is

**Calculation:**

Draw the diagram of a triangle with the vectors **a** and **b** as shown in Figure 1.

Here, **a**, **b** are the length of the other two sides of the triangles

(b)

To determine

**To prove:** The Triangle Inequality.

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