Find the curvature of r(t) = 9t. t2. t3 at the point (9. 1. 1).

Find the curvature of
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

Leave a Comment