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

Question

Relative to the origin $O$, the points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively. It is given that the magnitude of $\mathbf{a}$ is $4$ and $\mathbf{b}$ is a unit vector perpendicular to $\mathbf{a}$. Find the value of $\left( 2\mathbf{a}+\mathbf{b} \right)\cdot \left( 3\mathbf{a}-5\mathbf{b} \right)$.[4] The point $C$ is on $AB$such that $AC:CB=3:1$. Write down the position vector of $C$, $\mathbf{c}$, in terms of $\mathbf{a}$ and $\mathbf{b}$.[1] State the geometrical meaning of $\left| \mathbf{b}\times \mathbf{c} \right|$ and find its exact value.[5]

Accepted Answer

(i) ${91}$ (ii) ${\frac{\mathbf{a} + 3\mathbf{b}}{4}}$ (iii) ${1}$

2019 SAJC Promo Q4

2019 SAJC Promo Q4

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