Vector Planes & Orthogonality -- Help! I must be doing something really stupid, and I'll kick myself when you point it out, but I'm having difficulty with this question: Find the unit normal to the plane x + 2y – 2z = 15. What is the distance of the plane from the origin? OK, so I know I need three points in the plane to identify it. I found points: A = (15,0,0) B = (15,1,1) C = (13,2,1) They all seem to satisfy the equation, right? So now I find two nonparallel vectors in this plane: A->B = 0i + 1j + 1k A->C = -2i + 2j + 1k They do indeed join those points, right? So now I want to find an orthogonal vector, so I take the cross product by calculating the determinant of the 3x3 matrix: [i j k] [0 1 1] [-2 2 1] = (1-2)i - (-2-0)j + (0+2)k = -i + 2j + 2k This vector ought to be orthogonal to vectors A->B, A->C and B->C (and their negatives). But I try to test it with the usual method of adding up the parts and seeing if they result in zero, using A->C as my comparison vector: (-2 * -1) + (2 * 2) + (1 * 2) = 8 Why doesn't this equal zero? I have a feeling that the middle (j) term is wrong, because if that was (2 * -2) then the whole thing would equal zero, but I don't see where I've got my signs wrong in the method. Any help would be much appreciated. Cheers!