A curve C is given by a vector function rt 6 lessthanorequal

A curve C is given by a vector function r(t), 6 lessthanorequalto t lessthanorequalto 9|, with unit tangent T(t)|, unit normal N(t)|, and unit binomial B(t)|, Indicate whether the following line integrals are positive, negative, or zero by typing P, N, or Z as appropriate: integral_C T middot dr = integral_C N middot dr = integral_C B middot dr =

Solution

Realizing that r\'(t) will be in the same direction as T(t) so the dot product will be positive, while r\'(t) will be perpendicular to N(t) and B(t) so those dot products wil be 0.

A:P

B:Z

C:Z

Hope this helps!