Transpose problem

**ZachGriffin** · August 18th 2009, 01:55 AM

Hi guys,

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

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

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

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

However $Pf, i1f, i2f, and P2$ 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.

**ZachGriffin** · August 20th 2009, 08:30 PM

Hey guys,

I've tried expanding the equation out using the $Rcos(x - alpha)$ identity but still end up with 3 instances of x on that side of the equation for each component of the $x, y, z$ 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?

**ZachGriffin** · August 27th 2009, 03:59 PM

Anybody? I'm really stuck here

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