Find the length of the perpendicular from the origin to the plane Also write the unit normal vector from the origin to the plane.

Given :

Equation of plane :

To Find :

i) Length of perpendicular = d

ii) Unit normal vector =

Formulae :

1) Unit Vector :

Let be any vector

Then unit vector of is

Where,

2) Length of perpendicular :

The length of the perpendicular from the origin to the plane

is given by,

Given the equation of the plane is

Comparing the above equation with

We get,

& p = 39

Therefore,

= 13

The length of the perpendicular from the origin to the given plane is

Vector normal to the plane is

Therefore, the unit vector normal to the plane is