Find a unit vector perpendicular to both, `A=2hati+3hatj+hatk and B=hati-hatj+hatk`

Explanation

As we have rad `C=AxxB` is a vector is a vector perpendicular to both A and B. Hence a unit vector `hatn` perpendicular to A and B can be written as `hatn=(vecC)/(|C|)=(AxxB)/(|AxxB|)`
Here, `AxxB=|{:(hati, hatj, hatk),(2,3,1),(1,-1,1):}|`
`=hati(3+1)+hatj(1-2)+hatk(-2-3)=4hati-hat5k`
Further `|AxxB|= sqrt((4)^(2)+(-1)^(2)+(-5)^(2))= sqrt(42)`
`:.` the desired unit vector is
`hatn=(AxxB)/(|AxxB|)`
or `hatn=(1)/(sqrt(42))=(4hati-hatj-5hatk)`