We have seen that a vector$-$valued function r$($t$)$ that describes a line through a point P in the direction of v is given by r$($t$)=$OP $+$ tv$.$ Based on the intuition you developed in Preview Activity $9\mathrm{.}7\mathrm{.}1,$ what do you think the derivative r $($t$)$ is$?$ What is its direction relative to the line traced out by r$($t$)?$ What does it represent? Explain your reasoning.