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Math Help - Vector difficulties

  1. #1
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    Vector difficulties

    I am having some difficulties doing some basic vector questions on an assignment.

    a line L1 passes through (1,-1,4) and is parallel to vector (1,-1,1). Another line L2 passes through (2,4,7) and (4,5,10). obtain teh vector lines equations for L1 & L2. Do the two lines intersect, if so at what point?

    I think I have correctly worked out the line equations as:

    for L1: r = (1,-1,4)+
    λ(1,-1,1) Edit: thanks to plato
    for L2: r = (2,4,7)+
    λ(2,1,3)

    But I am unsure how to work out if they intersect, and if so where?

    Do i need to calculate their cartisan equations, and if so how do I then determine the intersect point.

    Thanks for your time
    Last edited by nickskely; February 24th 2009 at 08:23 AM.
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  2. #2
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    Quote Originally Posted by nickskely View Post
    [I]a line L1 passes through (1,-1,4) and is parallel to vector (1,-1,1). Another line L2 passes through (2,4,7) and (4,5,10). obtain teh vector lines equations for L1 & L2. Do the two lines intersect, if so at what point?
    for L2: r = (2,4,7)+[/B]λ(2,1,3)
    The first line is \ell _{1`} :\left\langle {1, - 1,4} \right\rangle  + \lambda \left\langle {1, - 1,1} \right\rangle
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  3. #3
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    Thanks for that Plato, but I am still not sure how to proceed to work out if and where the lines intersect?
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  4. #4
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    Quote Originally Posted by nickskely View Post
    I am still not sure how to proceed to work out if and where the lines intersect?
    Write each line in parametric form using a different parameter:
    \ell _1 :\left\{ \begin{gathered}<br />
  x = 1 + \lambda  \hfill \\<br />
  y =  - 1 - \lambda  \hfill \\<br />
  z = 4 + \lambda  \hfill \\ <br />
\end{gathered}  \right.\;\& \,\ell _2 :\left\{ \begin{gathered}<br />
  x = 2 + 2\mu  \hfill \\<br />
  y = 4 + \mu  \hfill \\<br />
  z = 7 + 3\mu  \hfill \\ <br />
\end{gathered}  \right.

    Now pick two of the coordinates and solve the equations.
    (Be sure you check the solution in the coordinate that was not used.)
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  5. #5
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    Thanks, but I am still unclear...

    are you saying I need to find the value of λ and μ that will make X (if chosen) equal for both coordiantes?

    thanks in advance
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  6. #6
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    Solve the system: \begin{gathered}  1 + \lambda  = 2 + 2\mu  \hfill \\   - 1 - \lambda  = 4 + \mu  \hfill \\ \end{gathered} .

    But make sure that it also works in 4 + \lambda  = z = 7 + 3\mu .
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  7. #7
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    ok, I see now

    So I got:

    λ = -3
    μ = -2

    and it also satisfies Z

    So is -3,-2 my intersection point?

    and what would the Z value be?
    -3,-2,0?

    thanks again
    Last edited by nickskely; February 24th 2009 at 11:21 AM.
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