Let

$u=\left[\begin{array}{c}1\\ 0\\ -2\end{array}\right],v=\left[\begin{array}{c}2\\ 1\\ 1\end{array}\right],$ and $w=\left[\begin{array}{c}4\\ -3\\ 4\end{array}\right].$

$($a$)$ Calculate the dot products vec$(u)*vec(v)$ and vec$(v)*vec(u)$ and vec$(u)*(vec(v)+$vec$(w)).$

$($b$)$ Compute the lengths $||u||,||v||$ and $||w||.$

$($c$)$ Verify triangular inequality $||vec(u)+$vec$(v)||||u||+||v||.$