The line P has equation
and we want to find the intersection of this line with the plane
We substitute the values of
from the line in terms of
into the equation of the plane. We solve this to find
then substitute this value ofback into the equation of the line to find the point of intersection.
Example: Find the point of intersection of
with the plane
From the line,
Substitute these expressions into the equation of the plane.
Substitute this value ofinto the equation of the line:
