Cross product imaginary numbers

[thegirl]

Hi,

I was just wondering if you have a cross product can you multiply out the constants and put them to one side.

So ik x ik x E is equal to i^2(k x k x E) therefore is equal to -k x k x E.

Is that correct?

 

[Orodruin]

Yes, the cross product is linear. However, writing something like A x B x C is not well defined as the cross product is not associative. You have to write either A x ( B x C) or (A x B) x C. Generally (k x k) x E = 0 while k x (k x E) will be non-zero if k and E are not parallel.

 

[thegirl]

Ahhhh yes the brackets! Thank You!