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Dot product and cross product problem

  1. Oct 13, 2009 #1
    I am having problems with this questions my physics teacher gave us. Since he doesn't explain things well, I do not know how he got an answer of 66. Can you please explain to me how to get this answer? THX.

    For the following three vectors, what is C*(A X 3B) (the "*" is suppose to be a dot)

    A = 4I -3J -2K B = -3I +1J +2K C = -3I + 5J -4K

    2. Relevant equations



    I J K I J
    4 -3 -2 4 -3
    -9 3 6 -9 3

    (18I+6I) + (18J-24J) + (-27K-12K)
    24I - 6J - 39K

    (24I X -3I) + (-6J X 5J) + (-39K X -4K)

    -72I -30J +156

    156-102

    54
     
  2. jcsd
  3. Oct 13, 2009 #2
    Do the cross product first, the three in front of B is a constant and can be pulled out of the cross product (or you can multiply three into all of the components of B, either works).

    Cross product by components:
    (A(J)*(B(K) - B(J)*A(K))I - (A(I)*B(K) - B(I)*A(K))J + (A(I)*B(J) - B(I)*A(J))K

    Then dot product is just multiplying each component and summing them.

    (A(I)*B(I)) + (A(J)*B(J)) + (A(K)*B(K)) and that should give you a number (or a scalar).

    I hope the notation makes sense. A/B then the I, J, or K component of that vector is inside of parentheses.

    Have fun with multivariate calc/linear algebra junk
     
  4. Oct 13, 2009 #3
    thank you I figured it out.
     
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