Find the torsion of the space curve.
-$$\mathbf { r } ( \mathrm { t } ) = ( 2 \mathrm { t } - 7 ) \mathbf { i } + \left( \mathrm { t } ^ { 2 } - 2 \right) \mathbf { j } + 7 \mathbf { k }$$
A) $\tau = - 1$
B) Undefined
C) $\tau = 1$
D) $\tau = 0$

Question

Quizplus · Accepted Answer

The torsion of a space curve measures how much the curve twists out of the plane of curvature. For the given curve, $\mathbf{r}(t) = (2t-7)\mathbf{i} + (t^2-2)\mathbf{j} + 7\mathbf{k}$, the z-component is constant (7$\mathbf{k}$), indicating that the curve does not twist out of its plane of curvature. Therefore, the torsion $\tau = 0$.

Find the Torsion of the Space Curve r(t)=(2t−7)i+(t2−2)j+7k\mathbf { r } ( \mathrm { t } ) = ( 2 \mathrm { t } - 7 ) \mathbf { i } + \left( \mathrm { t } ^ { 2 } - 2 \right) \mathbf { j } + 7 \mathbf { k }r(t)=(2t−7)i+(t2−2)j+7k

Find the Torsion of the Space Curve $\mathbf { r } ( \mathrm { t } ) = ( 2 \mathrm { t } - 7 ) \mathbf { i } + \left( \mathrm { t } ^ { 2 } - 2 \right) \mathbf { j } + 7 \mathbf { k }$