Everyone knows that the intersection of two planes in 3D is a line, and it’s easy to compute the line’s parameters. But, the cookbook formulae for the line are not necessarily the best nor most intuitive way of representing the line. This short note gives the derivation and the formula that I came up with when I was faced with this problem and couldn’t find a solution l liked anywhere. It is also a simple example of how to use Lagrange multipliers.