Find the vector equation of a plane whose Cartesian equation is 5x - 7y + 2z + 4 = 0.

Given :

Cartesian equation of the plane is

5x – 7y + 2z + 4 = 0

To Find : Vector equation of the given plane.

Formulae :

1) Dot Product :

If are two vectors

then,

Given the equation of the plane is

5x – 7y + 2z + 4 = 0

⇒ 5x – 7y + 2z = - 4

The term (5x – 7y + 2z) can be written as

But

Therefore the equation of the plane is

or

This is Vector equation of the given plane.