Question: 4 Equations, 4 Unknowns

My first equation is a vector equation which results in three separate equations and four unknowns:

W x V - [( A / |A|)* |W|*|V|*sqrt( 1 - b^2 * (|W|^2/|V|^2)] =0

Where W,V, and A are all vectors with three components.  The four unknowns are w[1], w[2], w[3], and also b.

The other equation i have is that w[1]^2 + w[2]^2 + w[3]^2 = |w|^2, where i know |w|^2.

This makes four equations and four unknowns.

I know v[1],v[2],v[3],a[1],a[2],a[3] and |w|.

The key is that w[1],w[2], w[3], and b must have solutions that are independent of each other i.e. they can only be made up of the known values.

How do I set these four equations up in maple in order for it to return the solutions for w[1],w[2],w[3], and b??

Any help would be appreciated.

Thanks.