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Find the position vector of $X$ in terms of $\mathbf{a}$ and $\mathbf{b}$. State your answer in its simplest form.
Mathematics 0580 · IGCSE · Vector geometry
Vector geometry — practice question
The figure depicts a parallelogram $OPQT$. The position vector of $P$ is $\mathbf{a}$ and the position vector of $T$ is $\mathbf{b}$. $K$ lies on $PQ$ such that $PK : KQ = 3 : 1$. The straight lines $OK$ and $TQ$ are produced until they intersect at $X$. The sketch is marked NOT TO SCALE.