1.

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.

Answer» `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`


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