Write the equation of the plane passing through the point (a, b, c) and parallel to the plane

Given :

A ≡ (a, b, c)

Equation of plane parallel to required plane

To Find : Equation of plane

Formulae :

1) Position vectors :

If A is a point having co-ordinates (a₁, a₂, a₃), then its position vector is given by,

2) Dot Product :

If are two vectors

then,

3) Equation of plane :

If a plane is passing through point A, then equation of plane is

Where,

Answer :

For point A ≡ (a, b, c), position vector is

As plane is parallel to the required plane, the vector normal to required plane is

Now,

= a + b + c

Equation of the plane passing through point A and perpendicular to vector is