1. ## Transpose problem

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.

2. Hey guys,

I've tried expanding the equation out using the $\displaystyle Rcos(x - alpha)$ identity but still end up with 3 instances of x on that side of the equation for each component of the $\displaystyle x, y, z$ vector. I'm really stuck here. No matter which way I look at it I can't seem to isolate X. I've tried using different identities but can't solve it. The original equation works when I substitute known data so it must be able to be transposed but I can't see it at the moment. Can somebody help?

3. Anybody? I'm really stuck here