A Level Maths Notes: C4 – Finding The Equation of a Plane Passing Through a Given Point Perpendicular to a Given Vector
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 for u by 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.
Example: Find the equation
of the plane perpendicular to the vector
passing through the point
Hence the equation of the
plane is
Notice
the coefficients are the components of the normal vector.