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