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.