Relative to the origin $O$, the position vectors of the points $A$, $B$ and $P$ are $-\mathbf{i}-3\m

Question

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 $\left( 1+2\lambda ight)\mathbf{i}+\left( \lambda -2 ight)\mathbf{j}+2\mathbf{k}$ respectively, where $\lambda \in \mathbb{R}$, $\lambda 
e -1$. Show that $A$, $B$ and $P$ are collinear. 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.

Accepted Answer

(i) Collinear (shown) (ii) $\lambda < -1$

2012 NJC P1 Q2

2012 NJC P1 Q2

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