Answer
$2\vec{u}=\langle0,-2\rangle$
$-3\vec{v}=\langle6,0\rangle$
$\vec{u}+\vec{v}=\langle-2,-1\rangle$
$3\vec{u}-4\vec{v}=\langle8,-3\rangle$
Work Step by Step
$\vec{u}=\langle0,-1\rangle,$ $\vec{v}=\langle-2,0\rangle$
$2\vec{u}$
Multiply both components of the vector $\vec{u}$ by $2$:
$2\vec{u}=2\langle0,-1\rangle=\langle0,-2\rangle$
$-3\vec{v}$
Multiply both components of the vector $\vec{v}$ by $-3$:
$-3\vec{v}=-3\langle-2,0\rangle=\langle6,0\rangle$
$\vec{u}+\vec{v}$
Add the same component from both vectors together and simplify:
$\vec{u}+\vec{v}=\langle0,-1\rangle+\langle-2,0\rangle=\langle0-2,-1+0\rangle=\langle-2,-1\rangle$
$3\vec{u}-4\vec{v}$
Multiply the vector $\vec{u}$ by $3$ and the vector $\vec{v}$ by $-4$, then add them together and simplify:
$3\vec{u}-4\vec{v}=3\langle0,-1\rangle-4\langle-2,0\rangle=\langle0,-3\rangle+\langle8,0\rangle=...$
$...=\langle8,-3\rangle$
