Consider the helix parametrized with the vector equation

Question

r(t)=cos t i+ sin t j + t k.
The length L of the helix between the points (1,0,0) and (1,0,6π) is equal to aπ. What is the value of a^2?

Answer 1

just plug in the formula:

s = ∫√(dx^2 + dy^2 + dz^2)
= ∫[0,6π] √(sin^2t + cos^2t + 1) dt
= √2 t [0,6π]
= 6√2 π
so, a^2 = 72