[In this question the unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and due north respectively.]
At time t=0t = 0t=0, a particle P P\,P is at position (−3i+7j)m(-3\mathbf{i} + 7\mathbf{j})\text{m}(−3i+7j)m relative to a fixed origin, OOO.
The particle moves with velocity (2i−8j)ms−1(2\mathbf{i} - 8\mathbf{j})\text{ms}^{-1}(2i−8j)ms−1
Find the speed of PPP.
Show that P P\,P passes through the point A A\,A with position (2i−13j)m(2\mathbf{i} - 13\mathbf{j})\text{m}(2i−13j)m.
Hence find the distance travelled by P P\,P before it reaches AAA.
Give your answer to 3 significant figures.
284 exam-style questions on Edexcel A Level Maths Vectors, covering 11.1 Vectors, 11.2 Representing Vectors, 11.3 Magnitude and Direction, 11.4 Position Vectors, 11.5 Solving Geometric Problems, and 11.6 Modelling with Vectors. Each one has a worked solution and a mark scheme showing where the marks go.