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Math Help - Vector: Coordinates and Parallel Lines

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    Vector: Coordinates and Parallel Lines

    This is part of a carried on question. I don't know how to do the posted part.Help would be appreciated.

    _______________________________________________


    Q:

    Referred to an origin O, the point A, B, C have coordinates (3, 2, 0), (1, 0, 1), (2, 2, 2) respectively.
    (i) Point D (4, 4, 1) lies on the plane. Show that AB and DC are parallel.
    (ii) Find the coordinates of the point where the line AC and BD meet.


    _______________________________________________

    Thanks in advance.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Air View Post
    This is part of a carried on question. I don't know how to do the posted part.Help would be appreciated.

    _______________________________________________


    Q:

    Referred to an origin O, the point A, B, C have coordinates (3, 2, 0), (1, 0, 1), (2, 2, 2) respectively.
    (i) Point D (4, 4, 1) lies on the plane. Show that AB and DC are parallel.
    find AC and DC and show that they are scalar multiples of each other
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Air View Post
    (ii) Find the coordinates of the point where the line AC and BD meet.


    _______________________________________________

    Thanks in advance.
    write AC and BD as (3-dimensional) lines. then equate corresponding components. you will get a set of simultaneous equations to solve. the solution will give you the point
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  4. #4
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    Quote Originally Posted by Air View Post
    Q:

    Referred to an origin O, the point A, B, C have coordinates (3, 2, 0), (1, 0, 1), (2, 2, 2) respectively.
    (i) Point D (4, 4, 1) lies on the plane. Show that AB and DC are parallel.
    (ii) Find the coordinates of the point where the line AC and BD meet.
    This question is nearly a trick question:

    Since

    |\overrightarrow{AB}| = |\overrightarrow{CD}| = 3

    you are dealing with a parallelogram. Therefore the point of intersection is the midpoint of AD or BC: M(2.5, 2, 1)
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