- #1
Mr Davis 97
- 1,462
- 44
This might seem like a naive question to ask, but a full explanation of why these two concepts are different would be welcome. I am confused because parametric equations are ##y = 8t^2## and ##x = 5t##, but at the same time, these two equations can describe the ##x## and ##y## components of a vector. Parametric differentiation is defined as ##\frac{\mathrm{d} y}{\mathrm{d} x} = \frac{\frac{\mathrm{d} y}{\mathrm{d} t}}{\frac{\mathrm{d} x}{\mathrm{d} t}}##, while vector differentiation is defined as ##\frac{\mathrm{d} \vec{r}}{\mathrm{d} t} = \left \langle \frac{\mathrm{d} x}{\mathrm{d} t}, \frac{\mathrm{d} y}{\mathrm{d} t} \right \rangle##