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Math Help - 3D points on line?

  1. #1
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    3D points on line?

    Hi guys, i have a question which seemed simple when i first read it but now i see for some reason i can't figure it out...

    i have three 3D points: A(5,1,3) B(7,9,-1) and C(1,-15,11)

    How can i determine if they are in a straight line?

    I think it has something to do with finding the distances between the points but after that I dont know what i'm doing. Any help would be appreciated. thank you!
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  2. #2
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    Quote Originally Posted by collegestudent321 View Post
    i have three 3D points: A(5,1,3) B(7,9,-1) and C(1,-15,11)
    How can i determine if they are in a straight line?
    There are several ways to proceed. Distance is one of them.
    However, I would use vectors.
    \overrightarrow {AB}  = \left\langle {2,8, - 4} \right\rangle \;\& \,\overrightarrow {AC}  = \left\langle { - 4, - 16,8} \right\rangle .
    Because, they are multiples of each other the points are colinear.
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  3. #3
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    oh ok. That makes sense. thank you!
    but out of curiosity... how would i do it with distances???
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  4. #4
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    Im asking because this section is BEFORE the vectors section, so technically this solution shouldnt use vectors.
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  5. #5
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    Quote Originally Posted by collegestudent321 View Post
    but out of curiosity... how would i do it with distances???
    Find the distances AB,~BC,~\&~AC.
    See if two of those add to the third.
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  6. #6
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    Oh ok, cool... Easy enough. Thanks!
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