Question

I would really appreciate if someone can help me in this homework problem. Suppose a curve C is parameterized by r (t) with a≤t≤b and suppose F ⃗ is a vector field F(t)=r (t)×r ' (t) for a≤t≤b. Find ∫F ⋅dr and explain your answer

Answer 1

Hint U x V is perpendicular to both U and V

Answer 2

F(t) is perpendicular to r'(t). Hence F.dr=0 everywhere so the the integral is zero

Answer 3

@eliassaab can you go in more detail please. I am kind of lost in this problem.

Answer 4

@eliassaab

Answer 5

@eliassaab when you say U and V what were you referring to? can you please clarify?

Answer 6

U and V are two vectors. The cross product of two vectors Ux V is perpendicular to U and V

Answer 7

So( UxV) . V =0
Hencr
(r(t) x r'(t)). dr= (r(t) x r'(t)). r'(t) dt = 0 dt =0