[In this question the horizontal unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and due north respectively.]
A model boat A A\,A moves on a lake with constant velocity (−i+6j) m s−1(-\mathbf{i} + 6\mathbf{j}) \text{ m s}^{-1}(−i+6j) m s−1. At time t=0t = 0t=0, A A\,A is at the point with position vector (2i−10j) m(2\mathbf{i} - 10\mathbf{j}) \text{ m}(2i−10j) m.
Find the speed of AAA.
Find the direction in which A A\,A is moving, giving your answer as a bearing.
At time t=0t = 0t=0, a second boat B B\,B is at the point with position vector (−26i+4j) m(-26\mathbf{i} + 4\mathbf{j}) \text{ m}(−26i+4j) m. Given that the velocity of B B\,B is (3i+4j) m s−1(3\mathbf{i} + 4\mathbf{j}) \text{ m s}^{-1}(3i+4j) m s−1, show that A A\,A and B B\,B will collide at a point P P\,P and find the position vector of PPP.
Given instead that B B\,B has speed 8 m s-1 and moves in the direction of the vector (3i+4j)(3\mathbf{i} + 4\mathbf{j})(3i+4j), find the distance of B B\,B from P P\,P when t=7 st = 7 \text{ s}t=7 s.
9 exam-style questions on Edexcel A Level Old Maths Vectors. Each one has a worked solution and a mark scheme showing where the marks go.