The lines defined by
\[\begin{pmatrix} 1 \\ -3 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 1 \\ 1 \end{pmatrix}\]and
\[\begin{pmatrix} -3 \\ 2 \\ -10 \end{pmatrix} + u \begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix}\]intersect at $P.$  Find the acute angle formed by the two lines at $P,$ in degrees.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The lines defined by
\[\begin{pmatrix} 1 \\ -3 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 1 \\ 1 \end{pmatrix}\]and
\[\begin{pmatrix} -3 \\ 2 \\ -10 \end{pmatrix} + u \begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix}\]intersect at $P.$  Find the acute angle formed by the two lines at $P,$ in degrees.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
60^\circ
The lines defined by
\[\begin{pmatrix} 1 \\ -3 \\ -1 \end{pmatrix} + t \begin{pmatrix} 2 \\ 1 \\ 1 \end{pmatrix}\]and
\[\begin{pmatrix} -3 \\ 2 \\ -10 \end{pmatrix} + u \begin{pmatrix} 1 \\ -1 \\ 2 \end{pmatrix}\]intersect at $P.$  Find the acute angle formed by the two lines at $P,$ in degrees.
train