A line passes through (2, -1, 3) and is perpendicular to the line $\overrightarrow {r} = ( {\hat{i} + \hat {j} - \hat{k}}) + \lambda (2\hat{i} - 2\hat{j} +\hat{k})$ and $\overrightarrow {r} = (2\hat{i} - \hat{j} -3\hat {k}) +\mu (\hat{i} + 2 \hat{j} +2\hat{k})$. Obtain its equation.

Question

$(A)\; \overrightarrow {r} = 2\hat{i} - \hat{j} +3\hat{k} \;+ \; \mu (2\hat {i} + 3 \hat{j} -2 \hat{k})$
$(B)\; \overrightarrow {r} = 2\hat{i} - \hat{j} +3\hat{k} \;- \; \mu (2\hat {i} - 3 \hat{j} +2 \hat{k})$
$(C)\; \overrightarrow {r} = 2\hat{i} - \hat{j} +3\hat{k} \;+ \; \mu (2\hat {i} - 3 \hat{j} -2 \hat{k})$
$(D)\; \overrightarrow {r} = 2\hat{i} - \hat{j} +3\hat{k} \;- \; \mu (2\hat {i} + 3 \hat{j} -2 \hat{k})$