Scalar equation of plane - three dimensional spaces, Mathematics

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Scalar Equation of Plane

A little more helpful form of the equations is as follows. Begin with the first form of the vector equation and write a vector for the difference.

{a, b, c} . ({x, y, z}  - {x0, y0, z0})  = 0

{a, b, c} . {x - x0, y - y0, z - z0} = 0

 Now, in fact compute the dot product to obtain,

a (x - x0) + b (y - y0) + c (z - z0) = 0

This is known as the scalar equation of plane. Frequently this will be written as,

ax + by + cz = d

in which d = ax0 + by0 + cz0

This second form is frequently how we are given equations of planes. 

Note: If we are given the equation of a plane in this form we can fast get a normal vector for the plane. A normal vector is as follow:

n = (a, b, c)


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