Referred to the origin $O$, the points $A$ and $B$ are such that $\overrightarrow{OA}=\mathbf{a}$ an

Question

Referred to the origin $O$, the points $A$ and $B$ are such that $\overrightarrow{OA}=\mathbf{a}$ and $\overrightarrow{OB}=\mathbf{b}$. The point $C$ on $OA$ is such that $OC:CA=1:2$ , the point $D$ on $OB$ is such that $OD:DB=3:4$ and the point $M$ on $CD$ is such that $11CM=5CD$. Find $\overrightarrow{OM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ .[3] By considering cross product, find the ratio of the area of triangle $OCM$ to the area of triangle $OAB$.[3]

Accepted Answer

(i) $\overrightarrow{OM}=\dfrac2{11}\mathbf a+\dfrac{15}{77}\mathbf b$ (ii) $5:77$

2014 HCI P2 Q3

2014 HCI P2 Q3

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