Question

Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane `vec r.(hati+hatj+hatk)=2`

Answer 1

The direction ratios of normal to the given plane `vec r.(hati+hatj+hatk)=2` are <1,1,1>

Therefore, the direction ratios of normal to the required plane are <1, 1, 1>.

So, the Cartesian equation of plane passing through (a, b, c) and having direction ratios <1, 1, 1> is 

1(x−a)+1(y−b)+1(z−c)=0

⇒x+y+z=a+b+c

The vector equation of the required plane is `vec r.(hati+hatj+hatk)=a+b+c`