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

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 $M$ is on $AB$ produced such that $AM:BM=4:1$ and the point $N$ is on $OB$ such that $ON:NB=2:3$ . Find $\overrightarrow{OM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.[2] By considering cross product, find the ratio of the area of triangle $ANB$ to the area of triangle $OAM$.[4]

Accepted Answer

(i) $\overrightarrow{OM}=\dfrac{4\mathbf b-\mathbf a}{3}$ (ii) $9:20$

2015 IJC P1 Q2

2015 IJC P1 Q2

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