1. The problem statement, all variables and given/known data Does the line through the point P(1, 2, 3) with direction vector d = (1, 2, -3) lie in the plane 2x+y-z=3? 2. Relevant equations 3. The attempt at a solution From the 2x+y-z i can get the vector (2, 1, -3) and the direction vector, their dot product does not equal zero. So, no it does lie on the plane. Just wondering if my intuition is correct.