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.
197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.