Vectors in problem solvingEdexcel A-Level Maths: Mind map

Exam questions on Vectors in problem solving

1. Relative to an origin $O$, the points $A$, $B$ and $C$ have position vectors $\mathbf{a}=\mathbf{i}+2\mathbf{j}$, $\mathbf{b}=5\mathbf{i}+3\mathbf{j}$ and $\mathbf{c}=8\mathbf{i}+7\mathbf{j}$. The quadrilateral $ABCD$ is a parallelogram.
   Find the position vector of the point where the diagonals $AC$ and $BD$ meet.2 marks
2. Two forces $\mathbf{F}_1=(5\mathbf{i}+2\mathbf{j})$ N and $\mathbf{F}_2=(-3\mathbf{i}+7\mathbf{j})$ N act on a particle, where $\mathbf{i}$ and $\mathbf{j}$ are unit vectors due east and due north. A third force $\mathbf{F}_3$ also acts, and the particle is in equilibrium.
   Find the angle that the resultant of $\mathbf{F}_1$ and $\mathbf{F}_2$ makes with the direction of $\mathbf{i}$, giving your answer to 1 decimal place.2 marks
3. At time $t=0$ a ship leaves a point with position vector $(2\mathbf{i}-5\mathbf{j})$ km relative to a port $O$, and then moves with constant velocity $(3\mathbf{i}+4\mathbf{j})$ km h$^{-1}$, where $\mathbf{i}$ and $\mathbf{j}$ are unit vectors due east and due north.
   Find the speed of the ship and its position vector after $t$ hours.3 marks