[미적분학1] Orthogonal

Two vectors \vec{a} and \vec{b} are orthogonal if and only if \vec{a}\cdot\vec{b} = 0

If |\vec{r}\left(t\right)|=c , then \vec{r}\left(t\right) is orthogonal to \vec{r}'\left(t\right) for all t

proof.

\vec{r}(t)\cdot\vec{r}(t) = |\vec{r}(t)|^2=c^2 \\ \Rightarrow 2\vec{r}'(t)\cdot\vec{r}(t) = 0\\\Rightarrow \vec{r}'(t)\cdot\vec{r}(t) = 0 \\ \Rightarrow \vec{r}'(t)\perp \vec{r}(t)