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Math Help - Perpendicular lines

  1. #1
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    Perpendicular lines

    This problem wasn't assigned to my class and is an even number so I wanted to make sure I was correct or even on the right track.

    Is line through (4, 1, -1) and (2, 5, 3) perpendicular to the line through (-3, 2, 0) and (5, 1, 4)?

    My solution:

    A = < 2 - 4, 5 - 1, 3 - -1>
    = <-2,4,4>
    B = <5 - -3, 1 - 2, 4 - 0>
    = <8,-1,4>


    A X B = <20,40,-30>

    <-2,4,4><20,40,-30> = 0
    <8,-1,4><20,40,-30> = 0

    They are perpendicular.
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  2. #2
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    Quote Originally Posted by kenshinofkin View Post
    This problem wasn't assigned to my class and is an even number so I wanted to make sure I was correct or even on the right track.

    Is line through (4, 1, -1) and (2, 5, 3) perpendicular to the line through (-3, 2, 0) and (5, 1, 4)?

    My solution:

    A = < 2 - 4, 5 - 1, 3 - -1>
    = <-2,4,4>
    B = <5 - -3, 1 - 2, 4 - 0>
    = <8,-1,4>


    A X B = <20,40,-30>

    <-2,4,4><20,40,-30> = 0
    <8,-1,4><20,40,-30> = 0

    They are perpendicular.
    A and B are vectors in the direction of the two lines.

    A.B = <-2,4,4> <8,-1,4> != 0 therefore the lines are >not< perpendicular.


    Note:

    A x B gives a vector perpendicular to A and B. I don't know why you've found it - it's irrelevant and has in fact completely mislead you into making a mistake.

    Because A x B is perpendicular to A and B it's no surprise that you get

    <-2,4,4><20,40,-30> = 0

    and

    <8,-1,4><20,40,-30> = 0.

    These results have absolutely nothing to do with the question.
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