Two distinct points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively, re

Question

Two distinct points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively, referred to an origin $O$. The point $P$ lies on $AB$ produced such that $AB:AP=2:3$. Express the position vector of $P$ in terms of $\mathbf{a}$ and $\mathbf{b}$. [2] Given also that $OP$ is perpendicular to $AB$ and that $OA:OB=2:1$, find the exact value of the cosine of the angle between $\mathbf{a}$ and $\mathbf{b}$. [4]

Accepted Answer

(i) $\vec{OP} = \frac{3\mathbf{b} - \mathbf{a}}{2}$, (ii) $\cos\theta = \frac{7}{8}$

2017 AJC J1 MYE Q7

2017 AJC J1 MYE Q7

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