We say that a line is parallel to a plane if the direction vector of the line is parallel to the plane. Let be the line containing the point
and parallel to the planes
Find a vector parametric equation for .
The normal vectors of the planes are and
. So, the direction vector
of
will be perpendicular to both of these,
From the first equation we have . Plugging this into the second equation we obtain
, which then gives us
. Since
is arbitrary, we take
to obtain a direction vector
. Therefore, the vector parametric equation for the line is
You can also obtain direction vector A by performing N1 X N2.