Find a unit vector perpendicular to both the vectors `(4hati+6hatj+2hatk) and (2hati-2hatj+4hatk)`.

Explanation

Let `vecA= 2hati+3hatj+hatk and vecB=hati-hatj+2hatk`
unit vector perpendicular to both `vecA and vecB` is `hatn = pm (vecA xx vecB)/(|vecAxx vecB|)`
`vecAxx vecB= |{:(hati,,hatj,,hatk), (2,,3,,1),(1,,-1,,2):}|= hati(6+1)-hatj(4-1)+hatk(-2-3)= 7hati-3hatj-5hatk`
`therefore |vecAxx vecB|= sqrt(7^(2) + (-3)^(2) + (-5)^(2))= sqrt(83)` unit `" "therefore hatn = pm (1)/(sqrt(83))(7hati-3hatj-5hatk)`