Find the curvature of

r(t) = 9t, t2, t3

at the point

(9, 1, 1)

r(t) = 9t, t2, t3

at the point

(9, 1, 1)

## Answer

curvature is | r’ x r”| / | r’ | ^3 r'(t) = <9,2t,3t^2> r”(t) = <0,2,6t> r’ x r” = <6t^2 , -54t , 18> at t = 1 , |r’ x r”| = sqrt(6^2 + 54^2 +18^2) = 57.24 |r’| = 9.7

| r’ x r”| / | r’ | ^3 = 57.24/9.7^3 = 0.063