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Vector Multiplication in a Triangle on the Cartesian Plane

  1. Aug 31, 2014 #1
    1. The problem statement, all variables and given/known data

    For the vectors in a Triangle, with a = 16, b = 12, and c = 20 what are

    (a) the magnitude and (b) the direction of A x B

    (c) the magnitude and (d) the direction of A x C

    (e) the magnitude and (f) the direction B x C

    this is Vector Multiplication.


    2. Relevant equations
    ABsin(ø)
    pythagorean theorem
    tan^-1 (y/x)



    3. The attempt at a solution

    16i x 12j = 192 (magnitude of A x B it is correct) and the direction is along the -x axis (believed)

    since this is vector multiplication, I realized that the best way to do it was using the determinant. which is a value associated with a square matrix. We can get the above relations following matrix algebra procedures to calculate the determinant of a 3×3 matrix, which in favor ends up giving us the vector product. if I am not mistaken the vector product can be expressed by multiplying the vectors, now here is where the problem arises. multiplying vector is not commutative and when multiplying vectors you get a new one (on the Z direction?)
     
  2. jcsd
  3. Aug 31, 2014 #2

    SteamKing

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    Staff Emeritus
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    Homework Helper

    You should learn the different results of the cross-products between the unit vectors.

    A handy mnemonic (a memory device) is

    i j k | i j

    which translated means (reading from left to right):

    i x j = k

    j x k = i

    k x i = j

    if you read the mnemonic in reverse, from right to left, you get:

    j x i = -k

    i x k = -j

    k x j = -i

    Any unit vector crossed with itself is zero:

    i x i = j x j = k x k = 0

    This can be confirmed also by writing out the cross products using determinants.
     
  4. Aug 31, 2014 #3
    ah Indeed thank you very much. surprise to find out that after all the attempts all of the answers were 192. and the directions were a little bit tricky but I got the right answer.

    thanks for the guidance.
     
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