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

Explanation

Let `veca=hati-2hatj+hatk` and `vecb=hati+2hatj+hatk`.Then,
`vecaxxvecb=|{:(hati,hatj,hatk),(1,-2,1),(1,2,1):}|=(-2-2)hati-(1-1)hatj+(2+2)hatk`
`=-4hati+4hatk`
`rArr " " vecaxxvecb=-4hati+4hatk`
`:. " "|vecaxxvecb|^(2)=4sqrt(2)`.
So, a unit vector perpendicular to both the vectors `veca` and `vecb` is given by
`hatn=(vecaxxvecb)/(|vecaxxvecb|)=(-4hati+4hatk)/(4sqrt(2))=(1)/(sqrt(2))(-hati+hatk)`