equation of line! please help!

Discussion in 'Physics & Math' started by yoda5412, May 18, 2008.

  1. yoda5412 Banned Banned

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    Hello!

    I have one problem which seems not so difficult:

    -Find the equation of line which passes throught the point M(1,0,7), parallel of the plane 3x-y+2z-15=0 and it intersects the line \(\frac{x-1}{4}=\frac{y-3}{2}=\frac{z}{1}\)

    The equation of the line will be: \(\frac{x-1}{a_1}=\frac{y}{a_2}=\frac{z-7}{a_3}\)

    So we need to find \(\vec{a}(a_1,a_2,a_3)\) and we need three conditions in the system.

    The first condition is \(\vec{a} \circ \vec{n}=0\) or \((a_1,a_2,a_3)(3,-1,2)=0\) or \(3a_1-a_2+2a_3=0\).

    The second condition is the intersection of two lines, and it is:

    \(-17a_1+28a_2+12a_3=0\)

    What about the third condition?
     
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  3. mathman Valued Senior Member

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    You don't need a third condition, since the a's are defined up to a constant multiplier. To solve, simply set one of them to 1 and solve for the other 2. As you wrote the original equation, none of the a's should be 0.
     
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  5. yoda5412 Banned Banned

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    And can \(\vec{a}=(a_1,a_2,a_3)=(0,0,0)\)?
     
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  7. mathman Valued Senior Member

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    NO!! At least one of the a's has to be non zero.
     
  8. yoda5412 Banned Banned

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    Why not?
     
  9. mathman Valued Senior Member

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    You won't have an equation for anything. You will have 0=0=0, or oo=oo=oo.
     

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