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Homework Help: Trouble with Cross Product

  1. Oct 30, 2008 #1
    1. The problem statement, all variables and given/known data
    Vector A = 3.5i + 1.8j and vector B = 1.7i + 4.8j . Find the components of A x B:


    2. Relevant equations
    AxB = AB sin(theta)


    3. The attempt at a solution
    Since vector A=3.5i+1.8j and B=1.7i+4.8j, I translated that into vectors. So, A is 3.94 @ 27.77*, and B is 5.09 @ 70.56*. This means that the angle between A and B is 42.79*.

    Using the AxB formula, I have 13.62. However, the problem (it's on WebAssign) wants the i, j, and k components.

    I tried the AxB formula with the individual i and j components, and I got 4.04 for the i direction, and 5.87 for the j direction. However, they're both wrong, and I have no idea how to find out the k direction...

    Help!

    Thanks in advance,
    -Angel.
     
  2. jcsd
  3. Oct 30, 2008 #2
    k is the third dimesion (or 3rd component in this case). A and B are 2 dimensions.
     
  4. Oct 30, 2008 #3
    I understand that the i, j, and k components are the x, y, and z directions, respectively. My frustration is that I believe I'm following the correct formula, but I still get the wrong answer. Where is my reasoning flawed?

    I have tried the following:
    AxB = (3.94)(5.09)sin(42.79) = 13.62, however, WebAssign wants the answer in components.
    So, I tried this:
    AxB = (3.5i)(1.7i)sin(42.79) = 4.04i

    and then
    AxB = (1.8)(4.8)sin(42.79) = 5.87j

    When I entered these two (out of three) answers, they were both marked wrong.
     
  5. Oct 30, 2008 #4
    The formula you try to use is for the magnitude of the vector axb, but the question asks for the vector itself.

    Do you know the way to calculate a cross product as if it were a determinant?

    axb=|i j k; a_i a_j a_k; b_i b_j b_k|
     
  6. Oct 30, 2008 #5
    When you cross two vectors the resultant vector will be orthogonal to both original vectors. Keep that in mind.
     
  7. Oct 30, 2008 #6
    You can multiply by components, but:

    i x i=0 (same for j x j)
    i x j =k
    j x i = -k

    Try this.
    Newer mind the sin. Multiply the two vectors as you'll do for two binomials.
     
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