Find the eqation of the plane passing through (a,b,c) and parallel to the plane `vecr.(hati+hatj+hatk)=2`

Answer

`hati+hatj+hatk` is a vector normal to the given plane. Since the required plane and the given plane are parallel, this vector will be a vector noraml to the required plane also. `therefore` The direction ratios of the normal to the required plane are 1,1,1.
Hence, the required equation is 1(x-a)+1(y-b)+1(z-c)=0
x-a+y-b+z=0 i.e., x+y+z=a+b+c