Answer
$(\vec{u}+\vec{v})\cdot(\vec{u}-\vec{v})=-5$
Work Step by Step
$\vec{u}=2\vec{i}+\vec{j}$ $,$ $\vec{v}=\vec{i}-3\vec{j}$ and $\vec{w}=3\vec{i}+4\vec{j}$
$(\vec{u}+\vec{v})\cdot(\vec{u}-\vec{v})$
Evaluate $\vec{u}+\vec{v}$ and $\vec{u}-\vec{v}$:
$\vec{u}+\vec{v}=(2+1)\vec{i}+(1-3)\vec{j}=3\vec{i}-2\vec{j}$
$\vec{u}-\vec{v}=(2-1)\vec{i}+(1+3)\vec{j}=\vec{i}+4\vec{j}$
Find $(\vec{u}+\vec{v})\cdot(\vec{u}-\vec{v})$ by multiplying corresponding components and adding:
$(\vec{u}+\vec{v})\cdot(\vec{u}-\vec{v})=(3)(1)+(-2)(4)=3-8=-5$
