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 $C$ lies on $OB$ such that $\overrightarrow{OC}=p\overrightarrow{OB}$, where $p$ is a constant. $D$ is on $AC$ such that $AD:DC=5:3$ and $E$ is on $AB$ such that $AE:EB=3:2$. Find $\overrightarrow{OD}$ and $\overrightarrow{OE}$ in terms of $\mathbf{a}$, $\mathbf{b}$ and $p$. [2] Given that $O$, $D$ and $E$ are collinear, find $p$. [3] Show that the area of the triangle $OAE$ can be expressed as $k\left| \mathbf{a}	imes \mathbf{b} ight|$, where $k$ is a constant to be determined. [3]

Accepted Answer

(i) $\overrightarrow{OD}=\dfrac38\mathbf a+\dfrac{5p}{8}\mathbf b$, $\overrightarrow{OE}=\dfrac25\mathbf a+\dfrac35\mathbf b$ (ii) $p=\dfrac9{10}$ (iii) $k=\dfrac3{10}$

JPJC Vectors Tutorial Q2

JPJC Vectors Tutorial Q2

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