Problems with vector questions

[aaron27]

Three vectors are expressed in terms of other three vectors
in the form of

a=a1α + a2β + a3γ
b=b1α + b2β + b3γ
c=c1α + c2β + c3γ

How to show that a.(bxc) = λ α.(βxγ) and find out λ?

I knew the first part where we carry out dot and product rule for vectors a.(bxc),
but the other side of the equation I have no idea how to start with.
Anyone knows how to do this?
Thanks.

 

[Simon Bridge]

Can you express each of the greek-letter vectors in terms of the latin-letter vectors?

 

[aaron27]

a=a1(alpha) + a2(beta) + a3(gamma)
b=b1(alpha) + b2(beta) + b3(gamma)
c=c1(alpha) + c2(beta) + c3(gamma)

How to show that a.(bxc) = λ (alpha) .(beta x gamma) and find out λ?

 

[Simon Bridge]

$\alpha = f(a,b,c)$
$\beta = g(a,b,c)$
$\gamma = h(a,b,c)$

what are f g and h?