Two lines are perpendicular.  One line has a direction vector of $\begin{pmatrix} 3 \\ -7 \end{pmatrix}.$  The other line has a direction vector of $\begin{pmatrix} a \\ 2 \end{pmatrix}.$  Find $a.$
Question:
Two lines are perpendicular.  One line has a direction vector of $\begin{pmatrix} 3 \\ -7 \end{pmatrix}.$  The other line has a direction vector of $\begin{pmatrix} a \\ 2 \end{pmatrix}.$  Find $a.$
Answer:
Let's think step by step.

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Two lines are perpendicular.  One line has a direction vector of $\begin{pmatrix} 3 \\ -7 \end{pmatrix}.$  The other line has a direction vector of $\begin{pmatrix} a \\ 2 \end{pmatrix}.$  Find $a.$
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