How to compute a tangent vector and arc length of a curve

An example on vector functions of one variable, including: tangent vector and arc length.

[DrChrisTisdell]

Yes, it's a definition, but not quite exactly the same as what you wrote. You are thinking of the case when the curve is given by y = f(x), with f a real-valued function.

[DeluxeWarPlaya]

Is the arc length you computed just a definition? Is that the same as int_t0^t1 sqrt(1+(r'(t))^2) dt