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Math Help - space

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    space

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  2. #2
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    Re: space

    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 B(x,y,z) is another point on the line that passes through A. Then, since this line is parallel to the x-axis, you know the difference of position vectors \vec{B}-\vec{A} is some scalar multiple of (1,0,0). Hence, y=-2,z=3. This gives a vector in the direction of your line that passes through point A to be (1,0,0). So, a line perpendicular to that could be (0,1,0), it could be (0,0,1). 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.
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