Answer
$2\vec{u}=4\vec{i}$
$-3\vec{v}=-9\vec{i}+6\vec{j}$
$\vec{u}+\vec{v}=5\vec{i}-2\vec{j}$
$3\vec{u}-4\vec{v}=-6\vec{i}+8\vec{j}$
Work Step by Step
$\vec{u}=2\vec{i},$ $\vec{v}=3\vec{i}-2\vec{j}$
$2\vec{u}$
Multiply both components of $\vec{u}$ by $2$:
$2\vec{u}=2(2\vec{i})=4\vec{i}$
$-3\vec{v}$
Multiply both components of $\vec{v}$ by $-3$
$-3\vec{v}=-3(3\vec{i}-2\vec{j})=-9\vec{i}+6\vec{j}$
$\vec{u}+\vec{v}$
Add the same component from both vectors together and simplify:
$\vec{u}+\vec{v}=(2\vec{i})+(3\vec{i}-2\vec{j})=(2+3)\vec{i}-2\vec{j}=5\vec{i}-2\vec{j}$
$3\vec{u}-4\vec{v}$
Multiply $\vec{u}$ by $3$ and $\vec{v}$ by $-4$, then add the two vectors together and simplify:
$3\vec{u}-4\vec{v}=3(2\vec{i})-4(3\vec{i}-2\vec{j})=(6\vec{i})+(-12\vec{i}+8\vec{j})=...$
$...=(6-12)\vec{i}+8\vec{j}=-6\vec{i}+8\vec{j}$