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Vectors and the Geometry of Space

  1. Oct 27, 2011 #1
    Line 1 and line 2 are given by equation 1 and 2. Point A has coordinates (xo, yo, zo). Find the equation of line 3 which goes through A and crosses L1 and L2.
     
  2. jcsd
  3. Oct 27, 2011 #2

    mathman

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    You failed to include equations 1 and 2.
     
  4. Oct 27, 2011 #3
    Equation 1 and 2 are not supposed to be given.
     
  5. Oct 28, 2011 #4

    LCKurtz

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    Suppose line 1 is R1(t) = P + tD1
    Line 2 is R2(s) = Q + sD2

    where the P and Q are given points and the D's are given direction vectors.

    Then a line from one to the other would be
    R3(u) = R1(t) + u(R2(s)-R1(t))

    Set that equal to your given point. You have three given coordinates of the point and three parameters s,t, and u to work with.
     
  6. Oct 28, 2011 #5
    I don't understand why you put R1(t) as the r0 vector in the R3(u) vector equation instead of just inputting the given point A there.
     
  7. Oct 28, 2011 #6

    LCKurtz

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    The line R3 goes from the line with parameter t to the other with parameter s with t and s unknown. You have to choose s and t so that it's possible for R3 to go through A for some value of u. For most choices of s and t the line won't pass through A for any value of u.

    [Edit -- Added] The general formula you get is long and messy but doing it for specific lines and points isn't too difficult.
     
    Last edited: Oct 28, 2011
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