Solve Equation of Fluid Dynamics

[Marco G]

Hi everybody ! 

I have the follow equation :

\qquad \mathbf{v}_l = \frac{1}{(1+A^2)}[\mathbf{B}-\mathbf{A}\times\mathbf{B} + (\mathbf{A} \cdot \mathbf{B}   ) \mathbf{A} ] 

look the pdf 

I would verify (but I don't have Mathematica or other symbolic computing package license) that is correct and if yes how to get this (the step) 

thanks in advance Marco

 

post2.pdf

[studiot]

Hello marco is this homework?

The pdf doesn't work

Just write it out by hand and post a scan or photograph.

[Marco G]

Sorry the pdf is here 

by the way is not a homework  i'm a pHD student 

[studiot]

For something of this complexity some explanation would be helpful. Especially description of the variables.

It's not clear what is known and what you are trying to get to.

You start with equation 1 and then state that one of the vectors (A) is a scalar times another vector s' in the second un-numbered equation.

The third equation is almost a substitution of this second equation into teh first, but is suddenly equated to vector B.

Where did this come from?

Then again you state "I've found this result", but not where or how.

[Marco G]

I found this equations in this paper