Let $a = \overrightarrow{i} -\overrightarrow{j} ; b = \overrightarrow{j} -\overrightarrow{k}; c = \overrightarrow{k} -\overrightarrow{i}$ if $\overrightarrow{d}$ is a unit vector such that $\overrightarrow{a} -\overrightarrow{d} =0= [b,c,d]$ then d equals

Question

$\begin{array}{1 1} \pm \large\frac{\overrightarrow{i}+\overrightarrow{j}-2 \overrightarrow{k}}{6} \\ \pm \large\frac{\overrightarrow{i}+\overrightarrow{j}- \overrightarrow{k}}{\sqrt 3} \\ \pm \large\frac{\overrightarrow{i}+\overrightarrow{j}+ \overrightarrow{k}}{\sqrt 3} \\ \pm \overrightarrow{k} \end{array}$