The vector equations of two lines $L_1$ and $L_2$ are respectively $\vec{r} = 17\hat{i} - 9\hat{j} + 9\hat{k} + \lambda(3\hat{i} + \hat{j} + 5\hat{k})$ and $\vec{r} = 15\hat{i} - 8\hat{j} - \hat{k} + \mu(4\hat{i} + 3\hat{j})$.

I. $L_1$ and $L_2$ are skew lines
II. $(11, -11, -1)$ is the point of intersection of $L_1$ and $L_2$
III. $(-11, 11, 1)$ is the point of intersection of $L_1$ and $L_2$
IV. $\cos^{-1}\left(\frac{3}{\sqrt{35}}\right)$ is the acute angle between $L_1$ and $L_2$

Then which of the following is true?