Referred to the origin $O$, points $P$ and $Q$ have position vectors $3\mathbf{a}$ and \(\ma

Question

Referred to the origin $O$, points $P$ and $Q$ have position vectors $3\mathbf{a}$ and $\mathbf{a}+\mathbf{b}$ respectively. Point $M$ is a point on $QP$ extended such that $PM:QM$ is $2:3$. Find the position vector of point $M$ in terms of $\mathbf{a}$ and $\mathbf{b}$.[2] Find $\overrightarrow{PQ}\times \overrightarrow{OM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.[3] State the geometrical meaning of $\frac{\left| \overrightarrow{PQ}\times \overrightarrow{OM} \right|}{\left| \overrightarrow{PQ} \right|}$.[1]

Accepted Answer

(i) $7\mathbf{a}-2\mathbf{b}$ (ii) $-3\mathbf{a}\times \mathbf{b}$ (iii) Shortest distance of point $O$ to line $PQ$.

2019 VJC P1 Q5

2019 VJC P1 Q5

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