Answer
$\vec{u}\cdot \vec{v}=0$
$||\vec{u}||^2=30$
$||\vec{v}||^2=101$
$||\vec{u}+\vec{v}||^2=131$
Work Step by Step
$\vec{u}\cdot \vec{v}=\vec{u}^T\vec{v}=-14+20-6=0$
$||\vec{u}||^2=\vec{u}\cdot\vec{u}=\vec{u}^T\vec{u}=4+25+1=30$
$||\vec{v}||^2=\vec{v}\cdot\vec{v}=\vec{v}^T\vec{v}=49+16+36=101$
$||\vec{u}+\vec{v}||^2=(\vec{u}+\vec{v})\cdot(\vec{u}+\vec{v})=\vec{u}^T\vec{u}+2\vec{u}^T\vec{v}+\vec{v}^T\vec{v}=131$
