NYJC/2021/JC2/Prelim/P1/Q01

The points $P$ and $Q$ have position vectors $p$ and $q$ respectively, which are non-zero and non-parallel. The points $P$ and $Q$ are fixed and $R$, with position vector $r$, varies.
(a) Given that $(2 r – p ) \times p = 0$, describe geometrically the set of all possible position vectors of $r$.

[2]

(b) If $r = q +\lambda p$, where $\lambda<0$, show that the area of $\triangle P Q R$ is $k| p \times q |$ where $k$ is a constant to be determined in terms of $\lambda$.

[3]