One line is parameterized by
\[\begin{pmatrix} 2 - 3t \\ -5 - 2t \\ 1 - 6t \end{pmatrix}.\]Another line is parameterized by
\[\begin{pmatrix} -\frac{3}{2} + s \\ 2s \\ -6 + 2s \end{pmatrix}.\]The two lines intersect at $P.$  If $\theta$ is the acute angle formed by the two lines at $P,$ then find $\cos \theta.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
One line is parameterized by
\[\begin{pmatrix} 2 - 3t \\ -5 - 2t \\ 1 - 6t \end{pmatrix}.\]Another line is parameterized by
\[\begin{pmatrix} -\frac{3}{2} + s \\ 2s \\ -6 + 2s \end{pmatrix}.\]The two lines intersect at $P.$  If $\theta$ is the acute angle formed by the two lines at $P,$ then find $\cos \theta.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{19}{21}
One line is parameterized by
\[\begin{pmatrix} 2 - 3t \\ -5 - 2t \\ 1 - 6t \end{pmatrix}.\]Another line is parameterized by
\[\begin{pmatrix} -\frac{3}{2} + s \\ 2s \\ -6 + 2s \end{pmatrix}.\]The two lines intersect at $P.$  If $\theta$ is the acute angle formed by the two lines at $P,$ then find $\cos \theta.$
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