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Vectors and Angles

  1. Apr 14, 2009 #1
    Hi,

    Suppose you have three vectors a, b and c.
    Say the angle between a and c is given by [tex]\alpha[/tex], and between b and c by [tex]\beta[/tex].

    Can we find a relationship between [tex]\alpha[/tex] and [tex]\beta[/tex]?

    Thanks in advance,
     
  2. jcsd
  3. Apr 14, 2009 #2
    Well, if you know dot products then you know:

    [tex]a . c = ||a|| ||c|| cos(\alpha)[/tex]
    [tex]b . c = ||b|| ||c|| cos(\beta)[/tex]

    So you could rearrange that to find a relationship between [tex]\alpha[/tex] and [tex]\beta[/tex].
     
  4. Apr 14, 2009 #3
    Thank you Whybother,

    Of course you are correct. But I'm wondering can a relation be found that does not involve the dot product? Perhaps if we think of the three vectors as the edge of a parallelepiped?
     
  5. Apr 14, 2009 #4
    Even if you are defining a parallelepiped in 3space, I don't think you can escape from the notion of dot and cross products. Looking at a http://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Parallelepiped_volume.svg/780px-Parallelepiped_volume.svg.png" [Broken] of it, it seems unavoidable to me.
     
    Last edited by a moderator: May 4, 2017
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