Mathematics

Problem

Let

\vec{a} = \hat{i} - \hat{j}

\vec{b} = \hat{j} - \hat{k}

and

\vec{c} = \hat{k} - \hat{i}

. If

\vec{d}

is a unit vector such that

\vec{a} \cdot \vec{d} = 0 = (\vec{b} \times \vec{c}) \cdot \vec{d}

, then

\vec{d}

is equal to a.

\pm \frac{(\hat{i} + \hat{j} - 2\hat{k})}{\sqrt{6}}

\pm \frac{(\hat{i} + \hat{j} - \hat{k})}{\sqrt{3}}

\pm \frac{(\hat{i} + \hat{j} + \hat{k})}{\sqrt{3}}

\pm \hat{k}