Find a unit vector perpendicular to both the vectors `2hati+3hatj+hatk) and (hati-hatj+2hatk)`.

Explanation

Let `vecA=2hati+3hatj+hatkandvecB=hati-hatj+2hatk`
unit vector perpendicular to both `vecAandvecB` is `hatn=(vecAxxvecB)/(|vecAxxvecB|)`
`vecAxxvecB=|(hati,hatj,hatk),(2,3,1),(1,-1,2)|=hati(6+1)-hatj(4-1)+hatk(-2-3)=7hati-3hatj-5hatk`
`therefore |vecAxxvecB|=sqrt(7^(2)+(-3)^(2)+(-5)^(2))=sqrt(83)` unit
`therefore hatn=(1)/(sqrt(83))(7hati-3hatj-5k)`