A Level Maths Notes: C4 – Finding The Perpendicular Line to a Plane Passing Through a Given Point
If a vector
is
perpendicular to a plane
then
it is perpendicular to every vector
and
line drawn in the plane, hence
We
can find an expression forby
subtracting one point in the plane from another. This is shown on the
diagram above as
where
is
an arbitrary point and
is
given, so by finding
or
we find the equation of the plane. Hence if the equation of a plane
is
a
normal is given by
If
the normal is to pass through the point
then
the line can be written:
Example: Find the equation
of the plane perpendicular to the plane 2x-4y-3z=17 passing through
the point
