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Math Help - need help fast

  1. #1
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    need help fast

    This was given in class to us

    Equation of a Plane

    From geometry, you learned that three distinct non-collinear points will determine a unique plane. Algebraically, the equation of the plane is given by Ax + By + Cz = D; thus, if the three distinct points were given, then we should be able to find the values of A, B, C, and D which will describe the equation of the plane passing through the points.

    Suppose the points P(1, 2, 4), Q(-2, 2, -2), and S(2, 1, 3) are the three distinct points determining the plane PQS. Write the algebraic representation for the plane containing these points.

    Your solution is due Wednesday, 3/18 by the beginning of class!

    i don't exactly understand how to approach this problem
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  2. #2
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    Quote Originally Posted by ruthvik View Post
    This was given in class to us

    Equation of a Plane

    From geometry, you learned that three distinct non-collinear points will determine a unique plane. Algebraically, the equation of the plane is given by Ax + By + Cz = D; thus, if the three distinct points were given, then we should be able to find the values of A, B, C, and D which will describe the equation of the plane passing through the points.

    Suppose the points P(1, 2, 4), Q(-2, 2, -2), and S(2, 1, 3) are the three distinct points determining the plane PQS. Write the algebraic representation for the plane containing these points.

    Your solution is due Wednesday, 3/18 by the beginning of class!

    i don't exactly understand how to approach this problem
    (x_1, y_1, z_1) = (1, 2, 4)

    (x_2, y_2, z_2) = (-2, 2, -2)

    (x_3, y_3, z_3) = (2, 1, 3).


    Substitute these values into the equation Ax + By + Cz = D and you'll get 3 equations in 3 unknowns which you can solve.

    A + 2B + 4C = D

    -2A + 2B - 2C = D

    2A + B + 3C = D.


    Solve for A, B, C (your answer will be in terms of D).
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  3. #3
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    how many solutions should i be getting ?

    Thanks btw

    EDIT : im getting 5 = 1, and all these weird answers, not getting anything equal to d
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  4. #4
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    Quote Originally Posted by ruthvik View Post
    how many solutions should i be getting ?

    Thanks btw

    EDIT : im getting 5 = 1, and all these weird answers, not getting anything equal to d




    .


    Do R_2 + 2R_1 and R_3 - 2R_1.


    A + 2B + 4C = D

    4B + 2C = 2D

    -3B - 5C = -D


    Do \frac{R_2}{4}


    A + 2B + 4C = D

    B + \frac{1}{2}C = \frac{1}{2}D

    -3B - 5C = -D


    Do R_3 + 3R_2


    A + 2B + 4C = D

    B + \frac{1}{2}C = \frac{1}{2}D

    -\frac{7}{3}C = \frac{1}{2}D


    I take it now you can solve for A, B, C?
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  5. #5
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    Quote Originally Posted by Prove It View Post




    .


    Do R_2 + 2R_1 and R_3 - 2R_1.


    A + 2B + 4C = D

    4B + 2C = 2D

    -3B - 5C = -D


    Do \frac{R_2}{4}


    A + 2B + 4C = D

    B + \frac{1}{2}C = \frac{1}{2}D

    -3B - 5C = -D


    Do R_3 + 3R_2


    A + 2B + 4C = D

    B + \frac{1}{2}C = \frac{1}{2}D

    -\frac{7}{3}C = \frac{1}{2}D


    I take it now you can solve for A, B, C?
    nvm, finished, thanks a lot
    Last edited by ruthvik; March 17th 2009 at 05:24 PM.
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