Draw an example of a curve such that \(\vT\) does not exist at a point on your curve. Identify the point where \(\vT\) fails to exist. Explain both why the direction of travel does not exist at that point based on your plot and why the direction of turning will not exist at the same point.
Draw an example of a curve such that \(\vT\, '\) does not exist at a point on your curve but \(\vT\)does exist at that point. Identify the point at which \(\vT\, '\) fails to exist. Explain both why \(\vT\, '\) does not exist at that point based on your plot and why \(\vN\) does not exist at the same point.
Draw an example of a curve such that \(\vT\, '=\vec{0}\) at a point on your curve. Explain why \(\vT\, '=\vec{0}\) based on your plot and explain why \(\vN\) does not exist at the same point.
