(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.