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Homework Help: Two vectors and the angle between them.

  1. Oct 22, 2009 #1
    1. The problem statement, all variables and given/known data

    An electron follows a helical path in a uniform magnetic field given by B = (20i - 50j - 30k ) mT. At time t = 0, the electron's velocity is given by v = (17i - 32j + 53k ) m/s.

    (a) What is the angle ϕ between v and B?

    Now, I have the answer from help from someone else. However, I don't understand the reasoning. The solution was to take: [tex]cos \phi = \frac{\vec v \cdot \vec B}{|\vec v| |\vec B|}[/tex] solving for ϕ.

    Can anyone explain it to me?
  2. jcsd
  3. Oct 23, 2009 #2


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    Science Advisor
    Homework Helper

    It's simply the formula for the dot product:

    for any vectors a and b,
    [tex]\vec a \cdot \vec b = |\vec a| |\vec b| \cos\phi,[/tex]
    where [itex]\phi[/itex] is the angle between the two vectors.
  4. Oct 23, 2009 #3
    OH! That NEVER occured to me.
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