The volume of a pyramid is
In three dimensional space all the vertices of the pyramid can be given coordinates.
The bass area can be expressed as the cross product of the vectors
and
The To find the height of the pyramid, notice that the cross product of two vectors is perpendicular to both vectors.and
define the base of the pyramid, so
is perpendicular to the base, and in the direction of the height. The height will be given by the component of
in the direction of the unit vector
This is equal to
Then