Three non-zero vectors $\mathbf{p}$, $\mathbf{q}$ and $\mathbf{r}$ are such that \(3\math

Question

Three non-zero vectors $\mathbf{p}$, $\mathbf{q}$ and $\mathbf{r}$ are such that $3\mathbf{p}\times \mathbf{q}=\mathbf{r}\times \mathbf{p}$. Find a linear relationship between $\mathbf{p}$, $\mathbf{q}$ and $\mathbf{r}$.[3] Referred to the origin $O$, the points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$. It is given that $\mathbf{a}$ and $\mathbf{b}$ are non-parallel unit vectors. The point $B$ divides $AC$ in the ratio $1:3$. The point $D$ lies on $OB$ produced such that $OB:OD=1:m$; $m\in \mathbb{Z}$; $m\ge 2$. Given that $\overrightarrow{AB}$ is perpendicular to $\overrightarrow{CD}$, find the numerical value of $m$.[4]

Accepted Answer

(a) $\mathbf{p}=k\left( 3\mathbf{q}+\mathbf{r} \right)$; $k\in \mathbb{R}\backslash \left\{ 0 \right\}$ (b) $m=7$

2024 CJC Promo Q7

2024 CJC Promo Q7

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