How to find the line of intersection of 2 planes
Cross product of directions, then eliminate one variable and solve for other two (most of the time get away with say x=0 but not if it is parallel to that)
Cross product form of a vector?
(r-a)xd=0
What does (r − a) × d = 0 represent?
The vector equation of a straight line, where a is a known point on the line, d is the direction vector, and r is the position vector of any point on the line
Vector equation of a plane (scalar product form)?
r . n = a . n, where n is the normal to the plane, a is a known point on the plane, and r is the position vector of any point on the plane
Cartesian equation of a plane?
ax + by + cz = d, where (a, b, c) is the normal vector n to the plane and d = n . p for any known point p on the plane
Parametric vector equation of a plane?
r = a + λb + μc, where a is a point on the plane, b and c are two non-parallel direction vectors lying in the plane, and λ, μ are scalar parameters
Vector equation of a line (parametric form)?
r = a + λb, where a is a known point on the line, b is the direction vector, and λ is a scalar parameter
