The position of a particle in space is for

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

Problem

The position of a particle in space is

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

for

0\le t\le 2\pi

. For which value(s) of

t

in this interval are the velocity and acceleration vectors orthogonal? (a)

t=\dfrac{\pi}{2}

only (b)

t=0,\,\pi,\,2\pi

t

[0,2\pi]

(d) No value of

t

[0,2\pi]