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Finding angles between vectors

  1. Apr 11, 2010 #1
    1. The problem statement, all variables and given/known data

    I have two related questions related because they both ask to find angles between vectors.

    The first one says to determine the angles between the sides of a parallelogram determined by the vectors OA = (3,2,-6) and OB = (-6,6,-2).

    The second one asks to determine the angle between OP and AE, where OP = (3,4,5) and AE = (-3,4,5).

    2. Relevant equations

    ?

    3. The attempt at a solution

    For the first one, I tried to use the cosine law, but got 1.5 degrees instead of 84.4 degrees.
    These are my steps.

    magnitude of OA = [tex]\sqrt{}(32 + 22 + -62) [/tex]= [tex]\sqrt{}49[/tex] = 7

    magnitude of OB = [tex]\sqrt{}](-62 + 62 + -22) [/tex]= [tex]\sqrt{}76[/tex]

    vector AB = (-9,4,4)

    magnitude of AB = [tex]\sqrt{}(-92 + 42 + 42)[/tex] = [tex]\sqrt{}113[/tex]

    [tex]\Theta[/tex] = cos-1 ((72 + [tex]\sqrt{}76[/tex] - [tex]\sqrt{}113[/tex]) / (2*7*[tex]\sqrt{}76[/tex])) = approximately 1.5 degrees

    I'm confused as to what to do here.

    The next question has me confused as well, as I seem to be missing something key.

    Please help!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 11, 2010 #2

    Mark44

    Staff: Mentor

    Don't put [ sup] or [ sub] tags inside [ tex] tags. The reason should be obvious.
    Your mixed tex and sup stuff is too hard to read, so I won't try to pick out the exact problem. Using the Law of Cosines (there's an easier way if you know about the dot product) and simplifying things a bit, you should get cos(theta) = 6/(7sqrt(76)). From this I get theta ~ 84.4 degrees. Make sure your calculator is in degree mode.
     
  4. Apr 11, 2010 #3
    thanks. It was in radian mode. whoops. But what about my second related question? Can I do the same thing? And I do know about dot product, but I'm supposed to do the question without it.
     
  5. Apr 11, 2010 #4

    Mark44

    Staff: Mentor

    Sure, the 2nd problem is almost exactly the same. The two sides adjacent to your angle are OP and AE.
     
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