Chapter 14, Problem 61RE

a.

To determine

To find: The unit tangent vector at all points of C.

b.

To determine

To find: The principal unit normal vector $N\left(t\right)$ and the curvature $\kappa$ of all points on C.

c.

To determine

To sketch: The curve $r\left(t\right)=\langle 3\sin t,3\cos t,4t\rangle$ and show that the unit tangent vector and the principal unit normal vector at all points of C corresponds to $t=0$ and $t=\frac{\pi }{2}$.

d.

To determine

To find: The result obtained in the part (a) and (b) are consistent with the graph shown in part (c).

e.

To determine

To find: The unit bi normal vector $B\left(t\right)$ at all points on the curve C.

f.

To determine

To plot: The unit normal vector $B\left(t\right)$ at the points of C corresponds to $t=0$ and $t=\frac{\pi }{2}$.

g.

To determine

To describe: The calculation to check the accuracy of the results in the parts from (a) to (f).

h.

To determine

To compute: The torsion at all points of curve C and interpret the result.