Find \(\vv\text{,}\) speed, and \(\vT\) as functions of \(t\) for the line parameterized as \(\vr(t)=\langle 3t-1,2-2t,5+t\rangle\text{.}\) Write a few sentences about why your results make sense and why in for this particular curve \(\vT\) does not vary based on the parameter value.
Consider a curve for which we do not know the parameterization. However, we do know that at a point \(P\text{,}\) the tangent line to the curve through \(P\) can be parameterized as \(\langle 2-7t, 3t+1,-4t-1\rangle\text{.}\) What are you able to say about \(\vT\) for this curve at the point \(P\text{?}\)
