Answer
$2\vec{u}=\langle-4,10\rangle$
$-3\vec{v}=\langle-6,24\rangle$
$\vec{u}+\vec{v}=\langle0,-3\rangle$
$3\vec{u}-4\vec{v}=\langle-14,47\rangle$
Work Step by Step
$\vec{u}=\langle-2,5\rangle,$ $\vec{v}=\langle2,-8\rangle$
$2\vec{u}$
Multiply both components of the vector $\vec{u}$ by $2$:
$2\vec{u}=2\langle-2,5\rangle=\langle-4,10\rangle$
$-3\vec{v}$
Multiply both components of the vector $\vec{v}$ by $-3$:
$-3\vec{v}=-3\langle2,-8\rangle=\langle-6,24\rangle$
$\vec{u}+\vec{v}$
Add the same component of both vectors together and simplify:
$\vec{u}+\vec{v}=\langle-2,5\rangle+\langle2,-8\rangle=\langle-2+2,5-8\rangle=\langle0,-3\rangle$
$3\vec{u}-4\vec{v}$
Multiply the vector $\vec{u}$ by $3$ and the vector $\vec{v}$ by $-4$ and then evaluate the operation:
$3\vec{u}-4\vec{v}=3\langle-2,5\rangle-4\langle2,-8\rangle=\langle-6,15\rangle+\langle-8,32\rangle=...$
$...=\langle-6-8,15+32\rangle=\langle-14,47\rangle$
