A boat B B\,B is moving with constant velocity. At noon, B B\,B is at the point with position vector (3i−4j)(3\mathbf{i} - 4\mathbf{j})(3i−4j) km with respect to a fixed origin OOO. At 1430 on the same day, B B\,B is at the point with position vector (8i+11j)(8\mathbf{i} + 11\mathbf{j})(8i+11j) km.
Find the velocity of BBB, giving your answer in the form pi+qjp\mathbf{i} + q\mathbf{j}pi+qj.
At time t t\,t hours after noon, the position vector of B B\,B is b\mathbf{b}b km. Find, in terms of ttt, an expression for b\mathbf{b}b.
Another boat C C\,C is also moving with constant velocity. The position vector of CCC, c\mathbf{c}c km, at time t t\,t hours after noon, is given by c=(−9i+20j)+t(6i+λj)\mathbf{c} = (-9\mathbf{i} + 20\mathbf{j}) + t(6\mathbf{i} + \lambda\mathbf{j})c=(−9i+20j)+t(6i+λj), where λ \lambda\,λ is a constant. Given that C C\,C intercepts BBB, find the value of λ\lambdaλ.
Show that, before C C\,C intercepts BBB, the boats are moving with the same speed.
Practise Edexcel A Level Old Maths Vectors with exam-style questions for A Level Old Maths. 9 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) 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.