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Question about determining the angles of triangle given two vectors

  1. Aug 1, 2016 #1
    <<Mentor note: Missing template due to originally being posted elsewhere>>

    Hello everyone.

    I have the following problem:

    Determine the angles of a triangle where two sides of a triangle are formed by the vectors

    A = 3i -4j -k and B=4i -j + 3k

    I thought that I would find the third side being represented by vector R which would be equal to A-B, that is
    R = -i -3j -4k.

    I would then take the cross products of each combination of the two vectors and find the angle between them and these would be the angles of the triangle.

    Dot producting A and B vectors, I get the angle between them to be 60 degrees.

    Dot producting the A and R vectors, I also get 60 degrees.

    Thus with the final angle = 180 - 60 - 60, the last angle should be 60 degrees also.

    This is blatantly wrong as my solutions tell me that the answer is:
    arcos 7 /sqrt(75), arcos sqrt(26)/sqrt(75), 90 degrees, or 36degrees4', 53degrees56', 90 degrees

    Could anyone please direct me as to what I did wrong and what mistakes need to be fixed? Thanks in advance.
    Last edited by a moderator: Aug 1, 2016
  2. jcsd
  3. Aug 1, 2016 #2


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    Your method and results are fine.
  4. Aug 1, 2016 #3

    Ray Vickson

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    Your solution is correct.

    However, a slightly easier way might have been to compute the lengths |A|, |B| and |R| = |A-B|; you would find these to all be equal, so your triangle is equilateral.
  5. Aug 2, 2016 #4
    Thank you everyone for your inputs. It is a relief to know that I did not mess something up.
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