2018 EJC Promo Q5
(a)
Given that $\mathbf{u}$ and $\mathbf{v}$ are non-zero vectors such that $\mathbf{u}\times \mathbf{v}=\left( \mathbf{u}-\mathbf{v} \right)\times \left( \mathbf{u}+\mathbf{v} \right)$, what can be deduced about $\mathbf{u}$ and $\mathbf{v}$?
[2]
(b)
Referred to an origin $O$, the points $A$ and $B$ have position vectors $\mathbf{a}$ and $\mathbf{b}$ respectively, where $\mathbf{a}$ and $\mathbf{b}$ are not parallel to each other. Point $C$ is the mid-point of $AB$. Point $D$ lies on $OA$ produced such that $OA:OD=1:p$, where $p>1$. Point $E$ lies on $BD$, between $B$ and $D$, such that $BE:ED=p:2$. Given that points $O$, $C$ and $E$ are collinear, find the value of $p$.
[4]
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