QUESTION $1[14=9$ marks$]$

A$)$ Consider a square with vertices $A,B,C,D.$ Suppose that vec$(AB)=5$vec$()$ and $D=(-2,1).$

Compute vec$(DB)*vec(DC).$

Find the coordinates of the point $Q.$

What is the vector projection of vec$(DQ)$ onto vec$(DC)?($multiple choices$)$

$($a$)$ vec$(DC)$

$($b$)2$vec$(DC)$

$($c$)\frac{1}{2}$vec$(DC)$

$($d$)\sqrt[\phantom{2}]{2}$vec$(DC)$

$($e$)\frac{1}{\sqrt[\phantom{2}]{2}}$vec$(DC).$