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Math Help - Algebraic Vectors

  1. #1
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    Algebraic Vectors

    Describe how you could use vectors to determine if 3 given points are collinear. Test your method using each set of points.

    i) P(-3, 1), Q(2, 4), R(5,6)

    ii) D(5,1), E(1, -5), F(-3,-11)

    I know how to find 2 points if they are collinear or not, but I don't know how to find 3 points that are collinear or not. . .so how would you determine them?

    I know. . .

     \frac {x_1}{x_2} = \frac {y_1}{y_2}
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  2. #2
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    Quote Originally Posted by Macleef View Post
    Describe how you could use vectors to determine if 3 given points are collinear. Test your method using each set of points.

    i) P(-3, 1), Q(2, 4), R(5,6)

    ii) D(5,1), E(1, -5), F(-3,-11)

    I know how to find 2 points if they are collinear or not, but I don't know how to find 3 points that are collinear or not. . .so how would you determine them?

    I know. . .

     \frac {x_1}{x_2} = \frac {y_1}{y_2}
    use 2 points to set up the equation of a straight line and test afterwards if the 3rd point is located on the line:

    PQ: (x,y) = (-3, 1) + r (5, 3) . If R(5, 6) lies on the line the coordinates of R must satuisfy the equation of the line:

    (5, 6) {\buildrel ? \over = }(-3,1) + r(5,3) . That means from

    5 = -3 + 5r ~\implies ~ r = \frac85 and from

    6 = 1 + 3r~\implies~ r = \frac53 there doesn't exist one value for r so that the point R is "produced" by the equation. Thus R \notin PQ

    I'll leave the next problem for you.


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