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Math Help - 2 vector calc questions

  1. #1
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    2 vector calc questions

    consider points p(2,1,3), q(1,2,1), R(-1,-1,-2), s(1,-4,0)
    Find the shortest distance between lines pq and rs

    Find the constant a so that the following vectors are coplanar
    2i-j+k i+2j-3k 3i-j+2k
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  2. #2
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    i need help please
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    Quote Originally Posted by leinadwerdna View Post
    consider points p(2,1,3), q(1,2,1), R(-1,-1,-2), s(1,-4,0)
    Find the shortest distance between lines pq and rs
    Is it clear to you these two lines are skew lines?
    The distance between two skew lines,  P + t\overrightarrow d \,\& \,R + s\overrightarrow e then the distance between them is:
     \frac{{\left| {\overrightarrow {PR}  \cdot \left( {\overrightarrow d  \times \overrightarrow e } \right)} \right|}} {{\left\| {\overrightarrow d  \times \overrightarrow e } \right\|}}
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    i dont understand
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    Quote Originally Posted by leinadwerdna View Post
    i dont understand
    Well if that is truly the case, do you think that you are ready to do this problem?
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    im not familiar with the notation u used
    what do the double bars in the denominator mean
    Last edited by leinadwerdna; February 9th 2010 at 03:10 PM.
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    Quote Originally Posted by leinadwerdna View Post
    im not familiar with the notation u used
    what do the double bars in the denominator mean
    Magnitude. Of course I'm also assuming he means the same with the single bars in the top. It essentially is the exact same thing as an "absolute value" sign.

    As for your second question, for three vectors to be coplanar, their scalar triple product must be 0. My problem, is I see no constant "a" in any of those vectors that one would have to solve for. Is their information missing from the problem.
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    The reason for the single bars on top is that the dot product is a number

    hence we have the absolute value of a number.

    On the bottom we have double bars because the cross product is a vector so we can talk about the magnitude of a vector but not the absolute value of a vector.
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    for the answer to this question i keep getting 16/square root of 53

    but the answer in the book is the 3root 2
    can someone confirm that i am right and the book is wrong this is driving me crazy
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  10. #10
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    could someone confirm i am doing this right
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