Chapter 11.3, Problem 11ES

The i, j, and k component of the “race vector� $\text{t}=1.2\text{i}+56\text{j}+13.1\text{k}$ denote the distance ( in miles) to swim, bike, and run in a Half Ironman triathelon. Suppose that ${\text{v}}_1,{\text{v}}_2,\text{and}{\text{v}}_3$ denote, respectively, the speeds $\left(\text{in}\text{mi}/\text{h}\right)$ of an athlete for each component and that $\text{w}={\text{v}}_1{}^{-1}\text{i}+{\text{v}}_2{}^{-1}\text{j}+{\text{v}}_3{}^{-1}\text{k}.$ What is an interpretation of the dot product $t\cdot w?$