AIEEE 2012 (Offline) 29th April Code AQuestion 1
Let $ABCD$ be a parallelogram such that $\overrightarrow{AB}=\vec q$, $\overrightarrow{AD}=\vec p$ and $\angle BAD$ be an acute angle. If $\vec r$ is the vector that coincides with the altitude directed from the vertex $B$ to the side $AD$, then $\vec r$ is given by :
Vector Algebra
Solution
The foot of the perpendicular from $B$ on $AD$ is $\frac{\vec p\cdot\vec q}{\vec p\cdot\vec p}\vec p$, so the altitude vector $B\to$foot is $\vec r=-\vec q+\frac{\vec p\cdot\vec q}{\vec p\cdot\vec p}\vec p$.