Vectors in problem solvingAQA A-Level Maths: Mind map

Exam questions on Vectors in problem solving

1. A particle of mass $2$ kg is acted on by two forces, $\mathbf F_1=(3\mathbf i+2\mathbf j)$ N and $\mathbf F_2=(-5\mathbf i+4\mathbf j)$ N, where $\mathbf i$ and $\mathbf j$ are perpendicular unit vectors.
   The force $\mathbf F_3$ is removed, so that only $\mathbf F_1$ and $\mathbf F_2$ act. Find the acceleration of the particle.2 marks
2. The points $P$, $Q$ and $R$ have position vectors $\mathbf p=\mathbf i+2\mathbf j$, $\mathbf q=3\mathbf i+8\mathbf j$ and $\mathbf r=k\mathbf i+14\mathbf j$, where $k$ is a constant.
   Given that $P$, $Q$ and $R$ are collinear, find the value of $k$.2 marks
3. Relative to a port $O$, the unit vectors $\mathbf i$ and $\mathbf j$ point due east and due north, and distances are in kilometres. At noon a ship is at the point with position vector $(8\mathbf i+6\mathbf j)$ km. It moves with constant velocity $(-2\mathbf i+\mathbf j)$ km h⁻¹.
   Find the position vector of the ship at 15:00 and its distance from $O$ at that time.3 marks