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Thread: Vector: Coordinates and Parallel Lines

  1. #1
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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 $\displaystyle O$, the point $\displaystyle A$, $\displaystyle B$, $\displaystyle C$ have coordinates $\displaystyle (3, 2, 0)$, $\displaystyle (1, 0, 1)$, $\displaystyle (2, 2, 2)$ respectively.
    (i) Point $\displaystyle D$ $\displaystyle (4, 4, 1)$ lies on the plane. Show that $\displaystyle AB$ and $\displaystyle DC$ are parallel.
    (ii) Find the coordinates of the point where the line $\displaystyle AC$ and $\displaystyle BD$ 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 $\displaystyle O$, the point $\displaystyle A$, $\displaystyle B$, $\displaystyle C$ have coordinates $\displaystyle (3, 2, 0)$, $\displaystyle (1, 0, 1)$, $\displaystyle (2, 2, 2)$ respectively.
    (i) Point $\displaystyle D$ $\displaystyle (4, 4, 1)$ lies on the plane. Show that $\displaystyle AB$ and $\displaystyle DC$ 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 $\displaystyle AC$ and $\displaystyle BD$ 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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    Quote Originally Posted by Air View Post
    Q:

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

    Since

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

    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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