Understanding the vector product

[Anden]

Homework Statement

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

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

 

[sara_87]

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))

 

[Anden]

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 ;)