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Unit vector cross products in different co-ords

  1. Apr 10, 2012 #1
    hey,

    i've been trying to work out how to determine the sign of cross products of unit vectors,

    for example in cylindrical,

    r x z = - theta

    theta x z = r

    r x theta = z

    i can't figure out the sign,

    r x z = |r||z|sinβ theta where β is the angle between them, which is 90°,

    and the length of the vectors are 1

    how can you tell that its actually -theta?
     
  2. jcsd
  3. Apr 10, 2012 #2

    BruceW

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    I can think of 3 different ways to figure this out. You are probably familiar with at least one of them. When you have a cross-product between two vectors, how do you usually work out the direction of the resulting vector?
     
  4. Apr 10, 2012 #3

    chiro

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    Science Advisor

    Hey Jesssa and welcome to the forums.

    Consider that a x b = |a||b|sin(a,b)N where N is the normal vector and also <a,b> = |a||b|cos(a,b) where a x b is the cross product and <a,b> is the dot or inner product for Cartesian three dimensional space.

    Now consider what sin(a,b) and cos(a,b) should be (in terms of sign) for the various quadrants.
     
  5. Apr 10, 2012 #4

    tiny-tim

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    i remember it by thinking that θ is in the same direction as y, and then using x x y = z etc :wink:
     
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