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

Question

Referred to the origin $O$, the points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ such that $$\mathbf{a} = \mathbf{i} + \mathbf{j} + \mathbf{k} \quad \text{and} \quad \mathbf{b} = \mathbf{i} + 2\mathbf{j} + 2\mathbf{k} .$$ Find the size of angle $OAB$.[2] The point $C$ has position vector $\mathbf{c}$ given by $\mathbf{c} = \lambda \mathbf{a} + \mu \mathbf{b}$, where $\lambda$ and $\mu$ are positive constants. Given that the area of triangle $OAC$ is twice that of triangle $OBC$, find $\mu$ in terms of $\lambda$,[3] hence, if $OC = \sqrt{118}$, find the position vector $\mathbf{c}$.[4]

Accepted Answer

(i) $144.7^\circ$ (ii) $\mu=2\lambda$ (iii) $\mathbf c=\begin{pmatrix}3\sqrt2\5\sqrt2\5\sqrt2\end{pmatrix}$

2021 JPJC P1 Q2

2021 JPJC P1 Q2

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