Answer
$(\vec{u}\cdot\vec{v})(\vec{u}\cdot\vec{w})=-10$
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 $(\vec{u}\cdot\vec{v})(\vec{u}\cdot\vec{w})$:
$(\vec{u}\cdot\vec{v})(\vec{u}\cdot\vec{w})=(-1)(10)=-10$
