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 11, with unit tangent T(f), unit normal N(t), and unit binormal 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

A)Since T and dr are in the same direction, T.dr is always positive. So the line integral is positive

B) Since kN = dT/dt. So N and dr are in opposite direction. So the line integral is negative

C) Since B = T x N, the B is perpendicular to both T and N. So B.dr will be zero. So the line integral is zero.