Vectors in two and three dimensionsEdexcel International A Level Maths: Mind map

Exam questions on Vectors in two and three dimensions

1. The points $A$ and $B$ have position vectors $\mathbf{a}=2\mathbf{i}-\mathbf{j}+3\mathbf{k}$ and $\mathbf{b}=5\mathbf{i}+3\mathbf{j}-\mathbf{k}$ relative to the origin $O$.
   Find a unit vector in the direction of $\overrightarrow{AB}$.2 marks
2. The points $A$ and $B$ have coordinates $(-1,2,3)$ and $(3,-2,5)$ relative to the origin $O$, and $M$ is the midpoint of $AB$.
   The point $C$ is such that $B$ is the midpoint of $AC$. Find the position vector of $C$.2 marks
3. Triangle $ABC$ has vertices $A(1,2,-1)$, $B(4,-2,3)$ and $C(5,5,3)$, where the coordinates are in metres. A calculator may be used.
   Show that triangle $ABC$ is isosceles.3 marks