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    • Thread Starter


    fairly easy vectors question, im looking for a nice, neat way to answer it. if anyone could help, that would be awesome.

    the plane P has equation r.(i + j - k) = 4
    the line l1, with equation r = 2i + 3j + k + t(-i + 2j + k) lies in the plane P.
    show that the line l2, with equation r = -i + 2j + 4k + s(-i + 2j + k) is parallel to the plane P.

    to me it seems fairly obvious that because l1 is parallel to l2, l2 must be parallel to P, but i wanted to say something less lame than that. i was thinking is there some way to use the scalar product to make it obvious?? help much appreciated - rep up for grabs, if you are in to that kind of thing...

    you can just say because the l1 and l2 have have the same direction vector they must be parallel, and since l1 lies in the plane they are are also parallel, i dont see the problem in this

    If you were being strict about it you would do the cross product of the two direction vectors of the lines and show that that does indeed come to zero.
    • Thread Starter

    i did it like that in the end, thanks.

    I just thought maybe there was a way of using the equation of the plane, but maybe not.

    Thank you!!! xx
    • Study Helper

    Study Helper
    Just a thought: Do you need to show that l2 is not in the plane, or are you allowed to include that as a possibility within "parallel to".
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