# 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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