Answer
$-71.57^{\circ}$
Work Step by Step
We're given that;
$\vec{a} = (3\,m)\hat{i}+(4\,m)\hat{j}$ and $\vec{b} = (5\,m)\hat{i}+(−2m)\hat{j}$.
We can subtract these vectors component-wise;
$\vec{b}-\vec{a} = (5\,m−3\,m)\hat{i}+(−2\,m−4\,m)\hat{j}$
$\vec{b}-\vec{a} =(2\,m)\hat{i}−(6\,m)\hat{j}$.
The angle then equals:
$\tan^{-1}(\frac{-6\,m}{2\,m}) = -71.57^{\circ}$.
