A particle P P\,P moves so that its position vector at time t t\,t seconds is
r=(3+2t)i+(4−t)j+(1+2t)k\mathbf{r} = (3 + 2t)\mathbf{i} + (4 - t)\mathbf{j} + (1 + 2t)\mathbf{k}r=(3+2t)i+(4−t)j+(1+2t)k
where the units of distance are metres.
Find the position vector of P P\,P when t=0t = 0t=0 and when t=3t = 3t=3.
Show that P P\,P moves in a straight line, and find the speed of PPP.
Find the exact distance of P P\,P from the origin when t=1t = 1t=1.
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.