Referred to the origin $O$, the points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b

Question

Referred to the origin $O$, the points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively. Point $C$ lies on $BA$ produced such that $AB:AC=3:2$. Find $\overrightarrow{OC}$ in terms of $\mathbf{a}$ and $\mathbf{b}$ and show that the area of triangle $OAC$ can be written as $k\left| \mathbf{a}	imes \mathbf{b} ight|$, where $k$ is a constant to be found. [3] Given that $\mathbf{a}$ and $\mathbf{b}$ are unit vectors and the magnitude of $\mathbf{a}+\mathbf{b}$ is $\sqrt{3}$, find the cosine of the angle between $\mathbf{a}$ and $\mathbf{b}$. [3]

Accepted Answer

(i) $k = \displaystyle\frac{1}{3}$; (ii) $\cos\theta = \displaystyle\frac{1}{2}$

2022 RI J1 CT Q2

2022 RI J1 CT Q2

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