For , which of the following is true about its curvature…

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For

\mathbf r(t)=\langle 2\cos t,\,2\sin t,\,3t\rangle

, which of the following is true about its curvature

\kappa(t)

? (a)

\kappa(t)=\dfrac{1}{2}

for all

t

. (b)

\kappa(t)=\dfrac{2}{\sqrt{13}}

for all

t

. (c)

\kappa(t)=\dfrac{2}{13}

for all

t

. (d)

\kappa(t)=\dfrac{2}{13}\cos t