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

Explanation

As we have read `C=AxxB` is a vector perpendicular to both A and B. Hence a unit vector `hatn` perpendicular to A and B can be writted 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-hatj-5hatk`
Further `|AxxB|=sqrt((4)^(2)+(-1)^(2)+(-5)^(2))=sqrt(42)`
`:.` The desired unit vectors is
`hatn=(AxxB)/(|AxxB|)" " or hatn=1/(sqrt(42))(4hati-hatj-5hatk)`