Find a unit vector ,`C=AxxB` is a vector perpendicular to both A and B Henc , a unit vector `hatn`perpendicular to A and B can be Written as
`hatn=(C)/(C)=(AxxB)/(|AxxB|)`
`Here, AxxB=|underset(1,-1,1)underset(2,3,1)hati,hatj,hatk|`
`=hati(3+1)+hatj(1-2)+hatk(-2-3)`
`=4hati-hatj-5hatk`
`Further, |AxxB|=sqrt((4)^(2)+(-1)^(2)+(-5)^(2))=sqrt(42)`
`therefore"the desired unit vector is "hatn=(AxxB)/(|AxxB|)`
`or hatn=(1)/(sqrt(42))(4hati -hatj+5hatk)`