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Math Help - determin arrangement of points in R3

  1. #1
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    determin arrangement of points in R3

    Given the points A(5,1,3), B(7,9,-1) , C(1, -15, 11) how do I determine if they are or not on a straight line?
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  2. #2
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    Quote Originally Posted by Craka View Post
    Given the points A(5,1,3), B(7,9,-1) , C(1, -15, 11) how do I determine if they are or not on a straight line?
    I know a couple of ways to show they are on the same line...

    1) Show the area of triangle formed by these points is 0.
    2) Form an equation of a line with two points and show the third satisfies it.
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  3. #3
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    Hello, Craka!

    Another method . . .


    Given the points: . A(5,1,3),\;B(7,9,\text{-}1),\;C(1, \text{-}15, 11)
    how do I determine if they are or not on a straight line?

    Find vector \overrightarrow{AB}\!:\;\;\overrightarrow{AB} \:=\:\langle 7-5,\:9-1,\:\text{-}1-3\rangle \:=\:\langle 2,\:8,\:\text{-}4\rangle \;=\;2\langle 1,\:4,\:\text{-}2\rangle

    Find vector \overrightarrow{BC}\!:\;\;\overrightarrow{BC} \:=\:\langle 1-7,\:\text{-}15-9,\:11-(\text{-}1)\rangle \:=\:\langle \text{-}6,\:\text{-}24,\:12\rangle \:=\: -6\langle1,\:4,\:\text{-}2\rangle <br />


    Since \overrightarrow{AB} \parallel \overrightarrow{BC},\;\;A,B,C \text{ are collinear.}

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