As shown in the diagram above, two planes intersect in a line. We can find the equation of the line by solving the equations of the planes simultaneously, with one extra complication – we have to introduce a parameter. If we take the parameter at being one of the coordinates, this usually simplifies the algebra.
Example: Find the equation of intersection of the planes
and
We take the parameter as
and put
The equations become
(1)
(2)
(1)-2*(2) gives
Substitute
into (2)
