Consider vectors $u=8i-6j$ and $v=6i+5j.$ Here you will show that $v$ can be decomposed as a sum $v=w+q$ where $w$ is parallel to $u$ and $q$ is perpendicular to $w.$ Enter your results using the component form of vectors.

$($a$)$ Compute $w=pro{j}_{u}v,$ the projection of $v$ onto $u.$

$w=$

$($b$)$ Compute $q=v-w$

$q=$

$($c$)$ Verify that $w,q$ are orthogonal.

$w*q=$

$($d$)$ Verify that the sum of $w$ and $q$ is $v$

$w+q=$