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Math Help - Vectors

  1. #1
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    Vectors

    The question I have a problem with is this:

    1. The lines l1 and l2 have vector equations given by:

    r1 = 3i - j + 2k + λ(-2i + j + k)
    r2 = -2i + 9j - 2k + μ(5i - 2j + k)

    Find the values of λand μ when the vector r1 - r2 is perpendicular to both lines.

    2. Find the shortest distance between the two lines
    __________________________________________________ ___________
    I am getting the values of λand μ both zero, and I do not think it makes sense, since you wouldn't be able to work out part 2.

    Any help?

    Thanks in advance
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  2. #2
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    Quote Originally Posted by yobacul View Post
    The question I have a problem with is this:

    1. The lines l1 and l2 have vector equations given by:

    r1 = 3i - j + 2k + λ(-2i + j + k)
    r2 = -2i + 9j - 2k + μ(5i - 2j + k)

    Find the values of λand μ when the vector r1 - r2 is perpendicular to both lines.

    2. Find the shortest distance between the two lines
    As stated, this question makes no sense.
    Let 3,-1,2),~Q-2,9,-2),~M=<-2,1,1>,~\&~N=<5,-2,1>" alt="P3,-1,2),~Q-2,9,-2),~M=<-2,1,1>,~\&~N=<5,-2,1>" />.
    The vector M\times N is perpendicular to both lines.
    The distance between the two lines is \frac{{\left| {\overrightarrow {PQ}  \cdot \left( {M \times N} \right)} \right|}}{{\left\| {M \times N} \right\|}}.
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