Mathematics 4024 · O Level · Vector geometry

Vector geometry — practice question

$OPRQ$ forms a parallelogram, and $S$ lies on $PR$ so that $PS : SR = 1 : 3$. $\vec{OP} = \mathbf{p}$ and $\vec{OQ} = \mathbf{q}$.
(a(i))[1]

Express $\vec{PQ}$ using $\mathbf{p}$ and/or $\mathbf{q}$.

(a(ii))[1]

Express $\vec{QS}$ as simply as you can in terms of $\mathbf{p}$ and/or $\mathbf{q}$.

(b(i))[2]

Point $T$ is on the extension of $QS$ such that $\vec{QT} = \frac{4}{3} \vec{QS}$. Express $\vec{PT}$ as simply as possible in terms of $\mathbf{p}$ and/or $\mathbf{q}$.

(b(ii))[1]

What can you conclude regarding the points $O$, $P$ and $T$?

Worked solution & mark scheme

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