A Level Maths Notes: FP3 – Finding the Volume of a Pyramid Using Vectors
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