Explanation

(c)
Let $Q(\overrightarrow{q})$ be the foot of altitude drawn from ‘$P$’ to the plane $\overrightarrow{r} \bullet \overrightarrow{n} = 0$
$\Rightarrow \overrightarrow{q} - \overrightarrow{p} = \lambda\overrightarrow{n}\ \ \Rightarrow \overrightarrow{q} = \overrightarrow{p} + \lambda\overrightarrow{n}$
Also $\overrightarrow{q} \bullet \overrightarrow{n} = 0 \Rightarrow \ \left( \overrightarrow{p} + \lambda\overrightarrow{n} \right) \bullet \overrightarrow{n} = 0$
$\Rightarrow \lambda = - \frac{\overrightarrow{p} \bullet \overrightarrow{n}}{\left| \overrightarrow{n} \right|^{2}}\ \Rightarrow \overrightarrow{q} - \overrightarrow{p} = - \frac{\left( \overrightarrow{p} \bullet \overrightarrow{n} \right)}{\left| \overrightarrow{n} \right|^{2}}\overrightarrow{n}$
Thus, required distance $= \left| \overrightarrow{q} - \overrightarrow{p} \right| = \frac{|\overrightarrow{p} \bullet \overrightarrow{n}|}{|\overrightarrow{n}|} = |\overrightarrow{p} \bullet \widehat{n}|$