With reference to origin $O$, the points $A$, $B$, $C$ and $D$ are such that $\overrightarrow{OA}=\m

Question

With reference to origin $O$, the points $A$, $B$, $C$ and $D$ are such that $\overrightarrow{OA}=\mathbf{a}$, $\overrightarrow{OB}=\mathbf{b}$, $\overrightarrow{OC}=-\mathbf{a}$ and $\overrightarrow{OD}=-2b$. The lines $AB$ and $DC$ meet at $E$. Find $\overrightarrow{OE}$ in terms of $\mathbf{a}$ and $\mathbf{b}$.[4] Hence show that $\frac{BE}{AB}=3$.[1] Show that the lines $AC$ and $BD$ are perpendicular.[2]

Accepted Answer

(i) BE/AB = 3; (ii) 6a·b

2017 TJC P2 Q4

2017 TJC P2 Q4

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