Find the curvature of the curve r(t).
-r(t) = (8 + cos 9t - sin 9t)i + (5 + sin 9t + cos 9t)j + 7k
A) $\kappa = \frac { \sqrt { 2 } } { 2 }$
B) $\kappa = \sqrt { 2 }$
C) $\kappa = \frac { 9 } { 2 }$
D) $\kappa = \frac { 9 } { 2 } \sqrt { 2 }$

Question

Find the curvature of the curve r(t).
-r(t) = (8 + cos 9t - sin 9t)i + (5 + sin 9t + cos 9t)j + 7k 
A) $\kappa = \frac { \sqrt { 2 } } { 2 }$
B) $\kappa = \sqrt { 2 }$
C) $\kappa = \frac { 9 } { 2 }$
D) $\kappa = \frac { 9 } { 2 } \sqrt { 2 }$

Quizplus · Accepted Answer

The curvature is given by the formula $\kappa = \frac { \left \| r'(t) \times r''(t) \right \| } { \left \| r'(t) \right \|^3 }$. Plugging in the given values, we get:$\kappa = \frac { \left \| (-9\sin 9t - 9\cos 9t)i + (9\cos 9t - 9\sin 9t)j \right \| } { \left \| (8 + \cos 9t - \sin 9t)i + (5 + \sin 9t + \cos 9t)j + 7k \right \|^3 }$$\kappa = \frac { \sqrt { 2 } } { 2 }$

Find the Curvature of the Curve R(t) κ=22\kappa = \frac { \sqrt { 2 } } { 2 }κ=22​​

Find the Curvature of the Curve R(t) $\kappa = \frac { \sqrt { 2 } } { 2 }$