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!

Homework Help: Understanding the vector product

  1. Oct 3, 2009 #1
    1. The problem statement, all variables and given/known data

    I've recently encountered the cross-product while studying mathematics. I'm studying on my own so it has been quite difficult to get a proper answer, which is why I'm posting my question here.
    What I've difficulties understanding is why the vector product of two vectors in a plane yields a vector perpendicular to the two.
    I've also difficulties with why i x j = (-j x i) = k

    3. The attempt at a solution

    I have no idea why this is, the scalar product is quite easy to understand in comparison. I'm using "University Physics" for my studies, which says that I must combine the magnitude equation (C = ABsin(phi)), A x B = -B x A and the right hand rule.

    Now from what I can gather from the magnitude equation, the magnitude of C is equal to the area of the parallellogram formed by A and B, why is this so?

    A and B are vectors in a plane, and C is the resultant vector from the vector product.

    I need someone to give me a hint on this one, to get me going
  2. jcsd
  3. Oct 3, 2009 #2
    the vector i is simply (1,0,0) and j is (0,1,0).
    the rule for vector product is: say you have two vectors: x=(a,b,c) and y=(d,e,f)
    then the vector product is= ((bf-ce) , - (af-cd), (ae-bd))
    do this for i x j and you will see it equals (-jxi)=k
    (remember k=(0,0,1))
  4. Oct 3, 2009 #3
    Wow, I had completely forgotten about using the vector components. :P It makes perfect sense now, when I did as you described. Thanks for your help ;)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook