Which of the following expressions always equals the unit tangent vector for a…

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

Problem

Which of the following expressions always equals the unit tangent vector

\mathbf T(t)

for a differentiable vector-valued function

\mathbf r(t)

whose velocity

\mathbf r'(t)

is never zero? (a)

\mathbf r'(t)

(b)

\displaystyle \frac{d}{dt}\left(\frac{\mathbf r(t)}{|\mathbf r(t)|}\right)

(c)

\displaystyle \frac{\mathbf r'(t)}{|\mathbf r'(t)|}

(d)

\displaystyle \frac{\mathbf r''(t)}{|\mathbf r''(t)|}