   Chapter 12.3, Problem 62E

Chapter
Section
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 |a+b||a|+|b|.

Calculation:

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

Here, a+b is the length of the longest side of the triangle, and a, b are the length of the other two sides of the triangles

(b)

To determine

To prove: The Triangle Inequality.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Calculate y'. 26. y=sinx

Single Variable Calculus: Early Transcendentals, Volume I

#### x3a+b3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Find the derivatives of the functions in Problems 1-34. 33.

Mathematical Applications for the Management, Life, and Social Sciences

#### In Exercises 116, determine whether the argument is valid. p~qp_q~q

Finite Mathematics for the Managerial, Life, and Social Sciences

#### Using tan2 x = sec2 x − 1, ∫ tan3 x dx =

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 