The shortest distance ...

Level pending

Given the function \(f(t)\)

\(f(t)=\sqrt{1105t^{2}-356t+29}\)

which describes the distance between the two vectors \(P_{t}\) and \(Q_{t}\) - we would like to know:

What is approximately (rounded to two decimal figures) the minimum distance between vector \(P_{t}\) and vector \(Q_{t}\) ?

Additional information (not really necessary for solving this problem):

\(\vec{P_{t}Q_{t}}={5 - 32t \choose 2 - 9t}\)

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