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Homework Help: How do I calculate the angle between three-dimensional vectors?

  1. Jan 19, 2012 #1
    1. The problem statement, all variables and given/known data

    In organic chemistry, a methane molecule, CH4, is made of 4 hydrogen and one carbon atoms where each hydrogen is attached to a central carbon atom. The hydrogen atoms are located at a corner of a regular tetrahedron and the carbon is at the center. In coordinates where one of the carbon hydrogen bond is in the direction i^ + j^ + k^, an adjacent bond is in the i^ -j^ -k^. Calculate the angle between these two bonds.

    2. Relevant equations

    I know how to solve a dot (scalar) product and a cross (vector) product but I don't know if either of those two are relevant here.

    3. The attempt at a solution

    I really don't know where to begin. I've never had any physics before and now I find myself in a 300-level college physics class. Until last week I didn't know what a vector was. While I'm good at math, I have never worked with anything three-dimensional before and have no idea what formula to use to find this angle. The answer wouldn't be 180 degrees, would it? That's what I'm visualizing but it seems way too easy...
  2. jcsd
  3. Jan 19, 2012 #2


    Staff: Mentor

    they give you two vectors <1,1,1> and <1,-1,-1>

    what is the definition of a dot product and what is the definition of a cross product. they are relevant to solving your problem.
  4. Jan 19, 2012 #3
    The dot product of two vectors A and B is equal to |A|*|B|*cos(θ) where θ is the angle between A and B.
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