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Vector multiplication

  1. Aug 30, 2011 #1
    1. The problem statement, all variables and given/known data

    d1 = 4i - 2j + 4k
    d2 = -5i + 5j - k

    Find

    (d1 + d2) * (d1 x 3d2)


    2. Relevant equations



    3. The attempt at a solution

    My first step was to add d1 and d2, which results in
    -i + 3j + 3k

    I then multiplied d2 by 3 to get
    -15i + 15j - 3k

    My problem is multiplying d1 and 3d2. I'm a bit confused on how to get the angle.

    I believe the formula for the magnitude is absin(theta), however the angle is something I don't quite understand. It is also my understanding that I use the "Right hand test" to get the direction of C.

    I think I can find the magnitudes by squaring i, j, k, then adding them, then taking the square root, so I have a and b. What should I do to determine the angle between d1 and 3d2? I think I've done this before, but lacking a third dimension, so it was just a 2 dimensional triangle.

    EDIT: I just read the chapter again and got to a final answer of 0 for this problem. Agree?

    Thanks!
     
    Last edited: Aug 30, 2011
  2. jcsd
  3. Aug 30, 2011 #2

    Mark44

    Staff: Mentor

    Both of these look OK.
    Haven't you seen a formula for calculating the cross product using the coordinates of the two vectors. This formula uses something called a pseudo-determinant, with i, j, and k across the top row, and the coordinates for the two vectors in the next two rows.
    Yes, I agree.
     
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