Position vectors and distanceEdexcel A-Level Maths: Mind map

Exam questions on Position vectors and distance

1. Relative to an origin $O$, the points $A$ and $B$ have position vectors $\mathbf{a}=2\mathbf{i}+7\mathbf{j}$ and $\mathbf{b}=8\mathbf{i}-\mathbf{j}$.
   The point $M$ is the midpoint of $AB$. Find the position vector of $M$.2 marks
2. Relative to an origin $O$, the points $P$, $Q$ and $R$ have position vectors $\mathbf{p}=\mathbf{i}+2\mathbf{j}$, $\mathbf{q}=5\mathbf{i}+5\mathbf{j}$ and $\mathbf{r}=13\mathbf{i}+11\mathbf{j}$.
   Find the exact distance $PR$.2 marks
3. Relative to an origin $O$, the points $A$, $B$ and $C$ are the vertices of a triangle, with position vectors $\mathbf{a}=\mathbf{i}+2\mathbf{j}$, $\mathbf{b}=7\mathbf{i}+4\mathbf{j}$ and $\mathbf{c}=3\mathbf{i}+8\mathbf{j}$.
   Show that triangle $ABC$ is isosceles.3 marks