Answer
$\vec{u}\cdot\vec{v}+\vec{u}\cdot\vec{w}=9$
Work Step by Step
$\vec{u}=2\vec{i}+\vec{j}$ $,$ $\vec{v}=\vec{i}-3\vec{j}$ and $\vec{w}=3\vec{i}+4\vec{j}$
$\vec{u}\cdot\vec{v}+\vec{u}\cdot\vec{w}$
Find $\vec{u}\cdot\vec{v}$ by multiplying corresponding components and adding:
$\vec{u}\cdot\vec{v}=(2)(1)+(1)(-3)=2-3=-1$
Find $\vec{u}\cdot\vec{w}$ by multiplying corresponding components and adding:
$\vec{u}\cdot\vec{w}=(2)(3)+(1)(4)=6+4=10$
Evaluate $\vec{u}\cdot\vec{v}+\vec{u}\cdot\vec{w}$:
$\vec{u}\cdot\vec{v}+\vec{u}\cdot\vec{w}=-1+10=9$
