Answer
$2\vec{u}=\langle4,14\rangle$
$-3\vec{v}=\langle-9,-3\rangle$
$\vec{u}+\vec{v}=\langle5,8\rangle$
$3\vec{u}-4\vec{v}=\langle-6,17\rangle$
Work Step by Step
$\vec{u}=\langle2,7\rangle,$ $\vec{v}=\langle3,1\rangle$
$2\vec{u}$
Multiply both components of the vector $\vec{u}$ by $2$:
$2\vec{u}=2\langle2,7\rangle=\langle4,14\rangle$
$-3\vec{v}$
Multiply both components of the vector $\vec{v}$ by $-3$:
$-3\vec{v}=-3\langle3,1\rangle=\langle-9,-3\rangle$
$\vec{u}+\vec{v}$
Add the corresponding components from both vectors together:
$\vec{u}+\vec{v}=\langle2,7\rangle+\langle3,1\rangle=\langle2+3,7+1\rangle=\langle5,8\rangle$
$3\vec{u}-4\vec{v}$
Multiply the vector $\vec{u}$ by $3$ and the vector $\vec{v}$ by $-4$, then evaluate the operation:
$3\vec{u}-4\vec{v}=3\langle2,7\rangle-4\langle3,1\rangle=\langle6,21\rangle+\langle-12,-4\rangle=...$
$...=\langle6-12,21-4\rangle=\langle-6,17\rangle$
