Find all values of $a$ so that the lines specified by
\[\begin{pmatrix} 1 \\ 2 \\ a \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}\]and
\[\begin{pmatrix} 4 \\ 1 \\ 0 \end{pmatrix} + u \begin{pmatrix} 5 \\ 2 \\ 1 \end{pmatrix}\]are skew.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find all values of $a$ so that the lines specified by
\[\begin{pmatrix} 1 \\ 2 \\ a \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}\]and
\[\begin{pmatrix} 4 \\ 1 \\ 0 \end{pmatrix} + u \begin{pmatrix} 5 \\ 2 \\ 1 \end{pmatrix}\]are skew.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(-\infty,3) \cup (3,\infty)
Find all values of $a$ so that the lines specified by
\[\begin{pmatrix} 1 \\ 2 \\ a \end{pmatrix} + t \begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}\]and
\[\begin{pmatrix} 4 \\ 1 \\ 0 \end{pmatrix} + u \begin{pmatrix} 5 \\ 2 \\ 1 \end{pmatrix}\]are skew.
train