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Solving 2 vectors with cross product

  1. Nov 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Two vectors are given by A = -6 i + 5 j and B = 1 i + 4 j
    Find A X B (answer only in terms of i, j, k)
    Find the angle between A and B (answer is terms of degrees)

    2. Relevant equations
    All I was told was that if I set a 3x3 matrix like this:
    i j k
    -6 5 0
    1 4 0
    then AxB is the determinant

    3. The attempt at a solution
    I made the 3x3 matrix and found the determinant to be only -29 k, which I am told is correct.
    I have absolutely no idea on how to approach the angle problem. If I may ask, can someone get me started in the right direction for that problem?
     
  2. jcsd
  3. Nov 22, 2012 #2

    rock.freak667

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    Look up the definition of cross product (here).

    You will see that you can calculate AxB in terms of a unit vector.
     
  4. Nov 22, 2012 #3

    LCKurtz

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    Have you had the formula ##\vec a \cdot \vec b = |\vec a||\vec b|\cos\theta##? That might come in handy.
     
  5. Nov 22, 2012 #4
    Also:
    ##|\vec a \times \vec b| = |\vec a||\vec b|\sin\theta##
     
  6. Nov 23, 2012 #5
    Why thanks, you two! I vaguely remember the dot product equation from precalculus (all those years ago), but the cross product one I've never seen. Thanks!
     
  7. Nov 23, 2012 #6

    LCKurtz

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    You're welcome. I might add that since the angle between two vectors is always between 0 and ##\pi##, the dot product may be slightly more convenient because that is the principle range of the inverse cosine.
     
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