Hi guys,

I'm having a problem with transposing the equation below to make $\displaystyle Vf$ the subject:

$\displaystyle D = | Pf + i1f*Rf*cos(Vf) + i2f*Rf*sin(Vf) - P2 |$

$\displaystyle | |$ denotes the length of the vector as in $\displaystyle sqrt(x^2 + y^2 + z^2)$

I know the trig identity where $\displaystyle a*cos(x) + b*sin(x)$ is equal to $\displaystyle R*cos(x - alpha)$ where $\displaystyle R = sqrt(a^2 + b^2)$ and $\displaystyle alpha = atan(b/a)$ which would get rid of the two instances of $\displaystyle Vf$.

However $\displaystyle Pf, i1f, i2f, and P2$ are all 3D vectors which is where I'm having the problem. I can't see how I can transpose the equation to make Vf the subject. Is there another identity I'm missing?

Any help is much appreciated.