## Fundamentals of Physics Extended (10th Edition)

Published by Wiley

# Chapter 3 - Vectors - Problems - Page 57: 16b

#### Answer

$8.246\,m$.

#### Work Step by Step

We're given that $\vec{a} = (3\,m)\hat{i} + (4\,m)\hat{j}$ and $\vec{b} = (5\,m)\hat{i} + (-2\,m)\hat{j}$. We can add these vectors component-wise; $\vec{a}+\vec{b} = (3\,m+5\,m)\hat{i} + (4\,m-2\,m)\hat{j} = 8\,m\,\hat{i}+2\,m\,\hat{j}$. The magnitude then equals (by Pythagorean's theorem): $\sqrt{(8\,m)^2 + (2\,m)^2} = 8.246\,m$.

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