You write "the directrix of a line...". A directrix is the line perpendicular to the axis of symmetry of a parabola. So, unless the line that passes through point A is actually a parabola, you are just looking for a line that is perpendicular to another line. Next, which line is supposed to be parallel to the x-axis? If A is a point, you cannot find a vector that is perpendicular to it. You need to find a vector that is perpendicular to some line. So, you can write is another point on the line that passes through . Then, since this line is parallel to the -axis, you know the difference of position vectors is some scalar multiple of . Hence, . This gives a vector in the direction of your line that passes through point A to be . So, a line perpendicular to that could be , it could be . Since you are not given a parabola, it is difficult to know the specific perpendicular line the question is looking for. There is no axis of symmetry to compare it to.