# Knowing $\alpha$ and $\beta$, compute $\gamma$. $vers(\vec v)=(\cos\alpha,\cos\beta,\cos\gamma)$

Knowing that:

$\vec v=|\vec v| vers(\vec v)$

$\cos\alpha=\frac{\vec v \cdot \vec i}{|\vec v|\cdot|\vec i|}$

$\cos\beta=\frac{\vec v \cdot \vec j}{|\vec v|\cdot|\vec j|}$

$\cos\gamma=\frac{\vec v \cdot \vec k}{|\vec v|\cdot|\vec k|}$

Our teacher at college gave us the following theorem:

$vers(\vec v)=(\cos\alpha,\cos\beta,\cos\gamma)$

One of our homework exercises says the following:

Knowing $\alpha$ and $\beta$, compute $\gamma$.

How exactly is this done? Can someone point me in the right direction? Thank you very much!

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What is "vers(v)"? –  DonAntonio Oct 10 '12 at 18:33
I think he means versine, en.wikipedia.org/wiki/Versine, which is $\mathrm{vers}\theta=1-\cos\theta$. In terms of taking vers of a vector, I have no idea... –  Clinton Boys Oct 10 '12 at 22:32
vers(v) is the notation my teacher uses for versors. –  Grozav Alex Ioan Oct 11 '12 at 3:29