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
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
Point D D\,D has position vector (1q)\begin{pmatrix} 1 \\ q \end{pmatrix}(1q) and angle ABD=90∘ABD = 90^{\circ}ABD=90∘
Determine the value of qqq.
