Answer
$$\langle18,-13\rangle$$
Work Step by Step
To scale a vector in component form, multiply each component by the scale factor.
$$-3\vec{u}=-3\langle -5,3\rangle=\langle (-3)\times (-5),(-3)\times 3\rangle=\langle15,-9\rangle$$
$$-\frac{1}{2}\vec{w}=-\frac{1}{2}\langle 2,2\rangle=\langle (-\frac{1}{2})\times 2,(-\frac{1}{2})\times2\rangle=\langle-1,-1\rangle$$
To add vectors in component form, add x and y components separately.
$$-3\vec{u}+\vec{v}-\frac{1}{2}\vec{w}=\langle 15,-9\rangle+\langle 4,-3\rangle+\langle-1,-1\rangle=\langle 15+4-1,-9-3-1\rangle=\langle18,-13\rangle$$
