Algebraic Question: e(e*a) - e x (e x a) = 3a?

[KleZMeR]

ok, this is my first post here so i don't know what kind of questions i can ask, so i'll fire away...
e is unit vector, I'm showing a = e(e*a) - e x (e x a), where * is the dot-product and x is the cross product, i keep getting 3a, not a. Is my algebra off or?...

 

[robphy]

Can you show your work so we can see where you might be going wrong?

 

[KleZMeR]

well that's a lot of stuff, ok i'll try, these are simple matrix operations, i think my positive/negative alternating on row operations are ok when finding det a, but still, the rhs is where the problem must be because e(e*a)=a, right?? so

a= c1x + c2y + c3z

and taking both cross products, e x (e x a), because all scalars of e = 1 i get

c1 + c2 + c3 - ((c2-c1) - (c1-c3))x = 3c1
c1 + c2 + c3 - ((c3-c2) - (c2-c1))y = 3c2
c1 + c2 + c3 - ((c1-c3) - (c3-c2))z = 3c3

so is this not =3a ??

why was this question moved? did i post it in the wrong place?

 

[genneth]

Use vector identities instead.

a x (b x c) = (a.c)b - (a.b)c

 

[KleZMeR]

thanks