Verify that and solve the quadratic equation
I'm trying to figure out how to find the intersection of a line and a surface in 3-space. For example, what if I had the equation for a line in parametric form:
x = 1 + t
y = -2 + t
z = 1 - 2t
and a surface (of an ellipsoid) in parametric form:
x = 2*cos(u)*cos(v)
y = 2*cos(u)*sin(v)
z = sin(u)
where -pi/2<u<pi/2 and -pi<v<pi
How would I go about finding the intersection point?