Given :

d = 7

To Find : Equation of plane

Formulae :

1) Unit Vector :

Let be any vector

Then unit vector of is

Where,

2) Dot Product :

If are two vectors

then,

3) 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 normal vector

Unit vector normal to the plane is

Equation of the plane is

This is a vector equation of the plane.

Now,

= (x × 3) + (y × 5) + (z × (-6))

= 3x + 5y – 6z

Therefore equation of the plane is

This is the Cartesian equation of the plane.