Find the vector and Cartesian equations of a plane which is at a distance of 5 units from the origin and which has as the unit vector normal to it.

Given :

d = 5

To Find : Equation of a plane

Formulae :

1) Dot Product :

If are two vectors

then,

2) Equation of plane :

Equation of plane which is at a distance of 5 units from the origin and having as a unit vector normal to it is

Where,

For given d = 5 and ,

Equation of plane is

This is a vector equation of the plane

Now,

= z

Therefore, the equation of the plane is

This is - the Cartesian z = 5 equation of the plane.