2012 NJC P1 Q2
Relative to the origin $O$, the position vectors of the points $A$, $B$ and $P$ are $-\mathbf{i}-3\mathbf{j}+2\mathbf{k}$, $5\mathbf{i}+2\mathbf{k}$ and $\left( 1+2\lambda \right)\mathbf{i}+\left( \lambda -2 \right)\mathbf{j}+2\mathbf{k}$ respectively, where $\lambda \in \mathbb{R}$, $\lambda \ne -1$.
(i)
Show that $A$, $B$ and $P$ are collinear.
(ii)
Find the value of $\lambda $ such that $P$ is on the line $BA$ produced and area of triangle $OAP$ is $162\sqrt{5}$ square units. Give a reason for your choice.
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