Question

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

Answer 1

We know that if `vec C= vec A × vec B` then `vec C` is perpendicular to both `vec A` and `vec B`

So,what we need is just to find the cross product of the given two vectors.

So,`(hati+hatj-hatk)×(hati-hatj+hatk)=-hatk-hatj-hatk+hati-hatj-i=-2(hatk+hatj)`

So,the unit vector is `(-2(hatk+hatj))/(sqrt(2^2 +2^2))=-(hatk+hatj)/sqrt(2)`