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Math Help - Symetric Form of a Line in R3

  1. #1
    Member sinewave85's Avatar
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    Symetric Form of a Line in R3

    This should be a simple one:

    I know that the formula is

    \frac{x-x_{0}}{A} = \frac{y-y_{0}}{B}=\frac{z-z_{0}}{C}

    so long as A, B, and C are all non-zero numbers. But what if one of the direction numbers is zero? Do you just drop that part of the equation since it is undefined? For instance, if C is 0, then

    \frac{x-x_{0}}{A} = \frac{y-y_{0}}{B}?

    Or is the whole equation undefined?
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  2. #2
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    Hello, sinewave85!

    This should have been explained to you . . . at some time, by someone.


    I know that the formula is : . \displaystyle \frac{x-x_{0}}{a} \:=\: \frac{y-y_{0}}{b}\:=\:\frac{z-z_{0}}{c}

    But what if one of the direction numbers is zero?
    Do you just drop that part of the equation since it is undefined? .No

    Suppose the direction contains a zero: . \vec v \:=\:\langle 2,3,0\rangle


    Believe it or not, we are allowed to write this:

    . . . . . \displaystyle \frac{x-x_o}{2} \;=\;\frac{y-y_o}{3}\;=\;\frac{z-z_o}{0}



    The standard "excuse" is that those denominators are simply "holders"
    . . for the components of the direction vector.

    So that we are not really dividing by zero,
    . . we're just "storing" the zero there. . . LOL!
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  3. #3
    Member sinewave85's Avatar
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    Divide by zero: shocking! Thanks so much.

    (My text book only defines the equation for A, B, C explicitly all nonzero and nothing in my course material expanded on that.)
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  4. #4
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    the equation would be (x-x0)/A = (y-y0)/B, z=z0
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