Chapter 12.3, Problem 62E

Triangle Inequality The Triangle Inequality for vectors is $|a+b|⩽\left|a\right|+\left|b\right|$

(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 $|a+b{|}^2=(a+b)\cdot (a+b)$ and use Property 3 of the dot product.]