Vector Equation Help: Solve Radial Acceleration

[Jonnyb42]

I am reading a book, and I see the following mathematical statements:

[PLAIN]http://mynqa.com/Cargo/Untitled2.bmp
and I have worked it out and it makes sense.
Then another statement comes up, regarding the radial acceleration this time:
[PLAIN]http://mynqa.com/Cargo/Untitled.bmp
This second equation does not make sense to me, when I work it out myself, using the first equation which I had successfully worked out, I arrive at the right side but missing the term:
[PLAIN]http://mynqa.com/Cargo/term.bmp
where does this middle term come from?

I know I am not providing much information as to what the equation is expressing, that is because what I am asking is primarily mathematical. These are vectors. OH one thing to know however, in the book they define vectors with the up-arrow/hat as soley direction, (magnitude 1) and the vectors with arrows pointing to the side as normal vectors, and corresponding letters without anything overhead is magnitude.

Thanks for any help.

 

[Jonnyb42]

Well I found out why I wasn't getting that extra term, is it because I was foolishly considering r₁₂ a constant, when it is differentiable.