Question

Find the length parameter of the curve r(t)=⟨6cost,6sint,2t⟩ with base point at (6,0,0).

a. 6.32
b. 6.32t²
c. 6.32(t−1)
d. 6.32t

Answer 1

To find the length parameter of the curve r(t), we need to calculate the arc length between the base point and a specific point on the curve.

Step-by-step explanation:

To find the length parameter of the curve r(t) = 6cos(t), 6sin(t), 2t, we need to calculate the arc length between the base point (6,0,0) and a specific point on the curve.

The arc length formula for a curve in three dimensions is given by:

Length = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

By plugging in the corresponding derivatives for each component, we can integrate to find the length parameter.