Find a unit vector normal to the plane `vecr.(2hati-3hatj+6hatk)+14=0`.

Explanation

The equation of the given plane is
`vecr.(2hati-3hatj+6hatk)+14=0`.
`ltimplies vecr.(2hati-3hatj+6hatk)=-14 rArr vecr.(-2hati+3hatj-6hatk)=14`.
`rArr vecr.vecn=14`, where `vecn=(-2hati+3hatj-6hatk)`.
`rArr vecr.(vecn)/(|vecn|)=14/|vecn|`, where `|vecn|=sqrt((-2)^(2)+3^(2)+(-6)^(2))=7`
`rArr vecr.(-2hat+3hatj-6hatk)/(7)=14/7 rArr vecr.(-2/7hati+3/7hatj-6/7hatk)=2`.
Hence, the unit vector normal to the given plane is
`hatn=(--2/7hati+3/7hatj-6/7hatk)`.