# What is the unit vector that is orthogonal to the plane containing  (i + j - k)  and  ( i - j + k) ?

We know that if vec C= vec A × vec B then $\vec{C}$ is perpendicular to both $\vec{A}$ and $\vec{B}$
So,(hati+hatj-hatk)×(hati-hatj+hatk)=-hatk-hatj-hatk+hati-hatj-i=-2(hatk+hatj)
So,the unit vector is $\frac{- 2 \left(\hat{k} + \hat{j}\right)}{\sqrt{{2}^{2} + {2}^{2}}} = - \frac{\hat{k} + \hat{j}}{\sqrt{2}}$