The points A A\,A and B B\,B have position vectors (23)\begin{pmatrix} 2 \\ 3 \end{pmatrix}(23) and (4−1)\begin{pmatrix} 4 \\ -1 \end{pmatrix}(4−1) respectively.
The point C C\,C has position vector (1p)\begin{pmatrix} 1 \\ p \end{pmatrix}(1p), and ABC ABC\,ABC is a straight line. Find ppp.
The point D D\,D has position vector (1q)\begin{pmatrix} 1 \\ q \end{pmatrix}(1q), and angle ABD=90°ABD = 90°ABD=90°. Determine the value of qqq.