1. The problem statement, all variables and given/known If C is a smooth curve given by r(s)= x(s)i + y(s)j + z(s)k Where s is the arc length parameter. Then ||r'(s)|| = 1. My professor has stated that this is true for all cases the magnitude of r'(s) will always equal 1. But he wants me to PROVE it. ( of course not with an example) 2. Relevant equations r(s)= x(s)i + y(s)j + z(s)k r'(s)= x'(s)i + y'(s)j + z'(s)k 3. Attempt at the solution To be quite honest, usually with math problems I will have some sort of attempt to try and solve it. But when it comes to proofs... I seem to get stuck. Well I know I'm trying to prove that. ||r'(s)|| = 1 So the magnitude of r'(s) Will be given by SQRT[ x'(s)^2 + y'(s)^2 + z'(s)^2 ] After this I don't know what I can do to make it equal 1. Any help will be greatly appreciated!