Two particles, PPP and QQQ, move in the same horizontal plane.
Particle PPP is initially at rest at the point with position vector (5i+2j)(5\mathbf{i} + 2\mathbf{j})(5i+2j) metres and moves with constant acceleration (2i+3j) m s−2(2\mathbf{i} + 3\mathbf{j})\, \text{m}\,\text{s}^{-2}(2i+3j)ms−2.
Particle QQQ moves in a straight line, passing through the points with position vectors (2i+3j)(2\mathbf{i} + 3\mathbf{j})(2i+3j) metres and (6i+cj)(6\mathbf{i} + c\mathbf{j})(6i+cj) metres.
PPP and QQQ are moving along parallel paths.
Show that c=9c = 9c=9.
Find an expression for the position vector of PPP at time ttt seconds.
Hence, prove that the paths of PPP and QQQ are not collinear.
Practise AQA A Level Maths 1.13 J: Vectors with exam-style questions for A Level Maths. 122 questions covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
