1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    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


    User Avatar
    Staff Emeritus
    Science Advisor
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Vector Multiplication in a Triangle on the Cartesian Plane
  1. Cartesian vectors (Replies: 3)

  2. Vectors triangle (Replies: 1)