Find the vector equation of a plane which is parallel to the plane `vecr.(2hati-hatj+2hatk)=5` and passes through the point whose position vector is `(hati+hatj+hatk)`.

Explanation

Any plane parallel to the plane `vecr.(2hati-hatj+2hatk)=5` is given by `vecr.(2hati-hatj+2hatk)=q` for some constant q.
…………(i)
Since it passes through a point having position vector `(hati+hatj+hatk)`, we have
`(hati+hatj+hatk). (2hati+hatj+2hatk)=1 rArr q=(2-1+2)=3`.
Putting q=3 in (i), we get the required of the plane is `vecr.(2hati-hatj+2hatk)=3`.