Find the shortest distance between the line $l_ 1$ and $l_2$ given by: $\overrightarrow {r} = \hat{i} +2\hat{j} -4\hat{k} + \lambda (2 \hat{i} + 3 \hat {j} + 6 \hat {k}) and \overrightarrow {r }= 3\hat{i} + 3\hat{j} -5\hat{k} + \mu(2\hat{i} + 3\hat{j} + 6\hat{k}) $

Question

$(A)\; \frac{293}{7}$
$(B)\; -\frac{293}{7}$
$(C)\; - \frac{\sqrt{293}}{7}$
$(D)\; \frac{\sqrt{293}}{7}$