(a)[2]
Express $\vec{OP}$ in terms of $a$ and $c$, giving the answer in its simplest form.
(b(i))[2]
State $\vec{OX}$ in terms of $a$ and $c$, and simplify fully.
(b(ii))[2]
Find the ratio $OX : XP$.
Mathematics 0580 · IGCSE · Vector geometry
Vector geometry — practice question
In the figure, $OABC$ forms a parallelogram. The lines $OP$ and $CA$ meet at $X$, and $CP:PB = 2:1$. Also, $OA = \vec{a}$ and $OC = \vec{c}$. The sketch is not drawn to scale and uses arrows to show the vectors $\vec{a}$ along $OA$ and $\vec{c}$ along $OC$, with $X$ marked where the diagonals meet.