Angle in a 3-D Parallelogram

  1. 1. The problem statement, all variables and given/known data
    Parallelogram in 3d with vectors. Points: A(2,-1,4); B(1,0,-1); C(1,2,3); D(2,1,8)

    I need the interior angle at B in degrees.


    2. Relevant equations

    cos(theta) = (Vector1 dot product vector2) / (magnitude of v1 * magnitude of v2)


    3. The attempt at a solution

    I used vectors BA and BC. I got 39 degrees. The answer sheet that I have uses AB and BC as the vectors and gets 140 degrees. Which vectors should I use? The picture in the homework makes the angle at B look like one of the smaller angles in the parallelogram, but I know you shouldn't trust pictures, because they might not be drawn to scale.

    So, I know how to do the problem, I just don't know which vectors are the correct ones to use. Could someone also explain WHY the particular set of vectors should be used instead of the other set? Thank you very much!
     
  2. jcsd
  3. Dick

    Dick 25,852
    Science Advisor
    Homework Helper

    You did it right. The book did it wrong.
     
  4. Thank you! That problem has been eating at me for the past few days and driving me nuts!
     
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