Find the torsion of the space curve.
-$\mathbf { r } ( \mathrm { t } ) = ( \mathrm { t } - 9 ) \mathbf { i } + ( \ln ( \sec t ) + 8 ) \mathbf { j } - 10 \mathbf { k } , - \pi / 2

Question

Find the torsion of the space curve.
-$\mathbf { r } ( \mathrm { t } ) = ( \mathrm { t } - 9 ) \mathbf { i } + ( \ln ( \sec t ) + 8 ) \mathbf { j } - 10 \mathbf { k } , - \pi / 2 < \mathrm { t } < \pi / 2$
A) $\tau = - 1$
B) $\tau = 0$
C) $\tau = 1$
D) Undefined

Quizplus · Accepted Answer

The torsion $\tau$ of a space curve is zero if the curve lies in a plane. The given curve is a plane curve because the z-component is constant (-10), indicating no change in the z-direction.

Find the Torsion of the Space Curve A) τ=−1\tau = - 1τ=−1

Find the Torsion of the Space Curve A) $\tau = - 1$