(a) If
lies on both planes, then

and at the same time

(b) A plane with normal vector
containing the point
can be written in the form

Expanding the left side, we see that the components of
correspond to the coefficients of
. So the normal vector to
is
.
(c) Similarly, the normal to
is
.
(d) The cross product of any two vectors
and
is perpendicular to both of the vectors. So we have

(e) Solve the two plane equations for
.


By substitution,

Let
. Then
and

Then the intersection can be parameterized by equations

for
.
We can also set
or
first, then solve for the other variables in terms of the parameter
, so this is by no means a unique parameterization.