Dot product between cross products

[quietrain]

Homework Statement

show (axb) . (cxd) =
|a.c b.c|
|a.d b.d|

The Attempt at a Solution

i have no idea. i don't know if the lines at the side are modulus lines or matrix brackets

but it seems that it has something to do with distribution law.

but i can't start proving if i don't even understand what the right hand side of the equation is ><

thanks for help!

 

[irycio]

Right side is a determinant of this matrix. It's not so hard to prove, you could in example use Levi-Civita symbol to write your cross product, it goes in 3 steps afterwards.

 

[quietrain]

Right side is a determinant of this matrix. It's not so hard to prove, you could in example use Levi-Civita symbol to write your cross product, it goes in 3 steps afterwards.

oh i have done it. but i didn't use that symbol? thanks anyway!

 

[irycio]

Well, you don't have to use it, that's just my favourite way to deal with cross product stuff :).