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.