The Shortest Distance between a Line and a Point

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Consider the line \( l \) with vector equation, \( \vec{r} = \binom{6}{k} + \lambda \binom{-4}{2} \), and let \( P \) be the point \( (2, 4) \). One value of \( k \) will make the shortest distance between the point and the line \( l \), 7 units long. This value of \( k \) can be written in the form \( \frac{a}{b} \sqrt{c} + b \). What is the value of \( 3a+2b+c \)?

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