Two drones, U U\,U and VVV, are operating in an open three-dimensional test range.
Drone U U\,U is initially at rest at a point with position vector (4i−2j+7k)(4\mathbf{i} - 2\mathbf{j} + 7\mathbf{k})(4i−2j+7k) metres. It moves with a constant acceleration of (2i−4j+6k) m s−2(2\mathbf{i} - 4\mathbf{j} + 6\mathbf{k})\, \text{m}\,\text{s}^{-2}(2i−4j+6k)ms−2.
Drone V V\,V moves along a straight line path that passes through the points with position vectors (−1i+3j+2k)(-1\mathbf{i} + 3\mathbf{j} + 2\mathbf{k})(−1i+3j+2k) metres and (5i+dj+20k)(5\mathbf{i} + d\mathbf{j} + 20\mathbf{k})(5i+dj+20k) metres.
The drones are moving along parallel paths.
Show that d=−9d = -9d=−9.
Find an expression for the position vector of drone U U\,U at time t t\,t seconds.
Hence, prove that the paths of drones U U\,U and V V\,V are not collinear.
109 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.