## Fundamentals of Physics Extended (10th Edition)

$6.32\,m$
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 subtract these vectors component-wise. $\vec{b}-\vec{a} = (5\,m-3\,m)\hat{i} + (-2\,m-4\,m)\hat{j} = (2\,m)\hat{i}-(6\,m)\hat{j}$. The magnitude then equals (by Pythagorean's theorem): $\sqrt{(2\,m)^2 + (-6\,m)^2} = 6.32\,m$.