If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are position vectors of three non collinear points $A,B,C$ respectively, then the shortest distance of $A$ from $BC$ is ?

Question

$(a)\; \overrightarrow a.(\overrightarrow b-\overrightarrow c)\qquad(b)\; |\overrightarrow b-\overrightarrow c|\qquad(c)\; \sqrt {|\overrightarrow b-\overrightarrow a|^2-\bigg(\large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow c|}\bigg)^2}\qquad(d)\; None\:of\:these$