No I did not. That is the whole point.
Actually I have suspected that you are confused as to the difference in those two functions.
Here is an example. Two lines $\displaystyle \ell_1: P+t\vec{D}~\&~\ell_2: P+t\vec{E}$ where $\displaystyle \ell_1\not\|\ell_2$.
Then the angle between $\displaystyle \ell_1~\&~\ell_2$ is $\displaystyle \theta = \arccos \left( {\frac{{D \cdot E}}{{\left\| D \right\| \cdot \left\| E \right\|}}} \right)$.
Now if $\displaystyle \arccos \left( {\frac{{D \cdot E}}{{\left\| D \right\| \cdot \left\| E \right\|}}} \right)>0$ then $\displaystyle \theta$ is acute.
And if $\displaystyle \arccos \left( {\frac{{D \cdot E}}{{\left\| D \right\| \cdot \left\| E \right\|}}} \right)<0$ then $\displaystyle \theta$ is obtuse.
But if your question were to ask for the acute angle betwwen $\displaystyle \ell_1~\&~\ell_2$ then it is $\displaystyle \theta = \arccos \left( {\frac{{|D \cdot E|}}{{\left\| D \right\| \cdot \left\| E \right\|}}} \right)$.
If I remember correctly, I got a positive angle, alpha, when taking the inverse cosine and then did pi - alpha = theta, where cos(theta) gave me the correct answer.
Is there something wrong with what I just said (in the post I am writing right now)?