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.
168 exam-style questions on OCR (MEI) A Level Maths 1.11 Vectors, covering 1.11.1 Language of vectors in two dimensions, 1.11.2 Add, subtract and scale vectors, 1.11.3 Magnitude and direction of a vector, 1.11.4 Position vectors, 1.11.5 Distance between points by position vectors, 1.11.6 Vectors to solve problems, 1.11.7 Language of vectors in three dimensions (A-level only), and 1.11 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.