Find the unit vector perpendicular to plane ABC where the position vector of A,B and C are `2 hat i-hat j+hat k, hat i+hat j+2 hat k` and `2 hat i+3 hat k` respectively.

Explanation

`vec(AB)=vecB-vecA=hati+haty+2hatk`

`=-(2hati-hatj+hatk)=-hati+2hatj+hatk`

`vec(BC)=vecC-vecB=2hati+3hatk-hati-hatj-2hatk`

`=hati-hatj+hatk`

Perpendicular vector=`3hati+2hatj-1hatk`

Unit vector=`(vec(AB)*vec(BC))/(|vec(AB)*vec(BC)|)`

`=(3hati+2hatj-hatk)/sqrt(3^2+2^2+1^2`

`=(3hati+2hatj-hatk)/sqrt15`