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Math Help - perpendicular vectors

  1. #1
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    perpendicular vectors

    I need to evaluate if two lines are perpendicular and give a reason for my answer.

    So: To show that the lines are not perpendicular, I need to show by the dot product method that my calculation does not = 0. Because cos(0)=90, perpendicular lines.
    I have two lines below:
    I need to start with my components in (i, j, k) form.
    The angle between the lines is the angle between their directions. The directions are U and V.

    r1=j+ak +λ(2i+4j-3k)
    r2=4i+3j-6k+μ(i+5j+k)

    u=2i+4j-3k,
    v=i+5j+k,
    u.v=(2, 4, -3)(1, 5, 1)=(2+20-3)=19

    Is this enough or do I need to go further, i.e

    |u|=√2+4+3=3
    |v|=√2+20+3=5

    cosθ=u.v/|u|.|v|
    19/15=1.267

    θ=but when I inverse cos I get a mathematical error when I try to inverse cos this figure?
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  2. #2
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    If two lines do not intersect, can they be perpendicular?
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  3. #3
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    no
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  4. #4
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    Therefore, if the dot product of the vectors is 0, it is not necessarily true that the lines are perpendicular (in 3-D).
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  5. #5
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    ahh shoot! That was dumb. sorry
    its not:
    |u|=√2+4+3=3
    |v|=√2+20+3=5

    but
    |u|=√2+4+3=√29
    |v|=√2+20+3=√413

    cosθ=u.v/|u|.|v|
    19/√29.√413=1.17
    θ=80
    Therefore the lines are not perpendicular.

    Please excuse the dumb error.
    Last edited by stealthmaths; February 20th 2010 at 04:46 PM. Reason: invalid comment
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