Question

Let ?C be the vertically oriented helix with radius of 33 that starts at (3,0,0)(3,0,0) and ends at (3,0,3)(3,0,3) after two revolutions on [0,1][0,1].

a) Find a vector-valued function ?⃗:[0,1]→ℝ3r→:[0,1]→R3 whose graph is ?C.

Hint: The projection of ?C onto the ??xy-plane is the circle with radius 33 centred at (0,0,0)(0,0,0); the projection of ?C onto the ?z-axis is the line segment from (0,0,0)(0,0,0) to (0,0,3)(0,0,3).

b) Compute the first derivative ?⃗˙r→˙ of ?⃗r→.

c) Compute the length of ?.

Answer 1