1. The problem statement, all variables and given/known data Give a Cartesian equation of the given hyperplane The plane passing through (1,2,2) and orthogonal to the line x = (5,1,-1) + t(-1,1,-1) 2. Relevant equations 3. The attempt at a solution So I've looked at this for a few hours and still can't figure out how to do it. It's supposed to be x(sub1) - x(sub2) + x(sub3) = 1, but I can't understand how one gets that solution. I know there should be a system of equations, with one of the equations being (1,-1,1) (which is orthogonal to the line in the question) but how about the other equations? Is the other hyperplane used for the system (5,1,-1) - (1,2,2) or something? Someone please help?!