I was wondering when evaluating line curves, and C is given by something such as $y = x^2$, how do you find the parametrization $<t, t^2, 0>$ ? ( I understand how z was found but not so much x and y; like what is the actual algebra?)
When it comes to parametrization along a line (from a single point to another single point) I can find $r(t)$, but not so much when given an equation such as that one.