# Vector Long Questions (Question 2)

Question 2:
Given that   and  $\stackrel{\to }{CD}=\left(\begin{array}{c}m\\ 7\end{array}\right)$ , find
(a) the coordinates of A,
(b) the unit vector in the direction of  $\stackrel{\to }{OA}$ .
(c) the value of m if CD is parallel to AB .

Solution:
(a)
$\begin{array}{l}\stackrel{\to }{AB}=\stackrel{\to }{AO}+\stackrel{\to }{OB}\\ \left(\begin{array}{c}10\\ 14\end{array}\right)=\left(\begin{array}{c}x\\ y\end{array}\right)+\left(\begin{array}{c}4\\ 6\end{array}\right)\\ \left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}10\\ 14\end{array}\right)-\left(\begin{array}{c}4\\ 6\end{array}\right)\\ \stackrel{\to }{AO}=\left(\begin{array}{c}6\\ 8\end{array}\right)\\ \stackrel{\to }{OA}=\left(\begin{array}{c}-6\\ -8\end{array}\right)\\ A=\left(-6,-8\right)\end{array}$
(b)

(c)