Let `vecu= hati+hatj, vecv = hati -hatj and vecw = hati+2hatj+3hatk`. If `hatn` is a unit vector such that `vecu.hatn =0 and vecv.hatn=0` then find the value of `|vecw.hatn|`

Explanation

`hatn=a_(1)hati=a_(2)hatj+a_(3)hatk " where " a_(1)^(2)+a_(2)^(2)+a_(3)^(2)=1`
Given that `vecu.hatn=0 Rightarrowa_(1)+a_(2)=0`
`Also, vecv.hatn=0 Rightarrowa_(1)-a_(2)=0`
`a_(1)=a_(2)=0`
`a_(3)=1or-1`
`hatn=hatk or-hatk`
`|vecwhatn|=3`