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If you have a parametric equation ##x=t, y=t^2,z=t^3## (the equation is randomn)

What does ##\vec{r}=t\hat{i}+t^2\hat{j}+t^3\hat{k}## represent?

now if it represents the position vector or the vector connecting origin and a point on the curve, then will ##\frac{dr}{dt}## give the tangent to the curve?