Let $k$, $l$ be smooth functions from an interval $I$ into $\mathbb R$ and $k>0$. Let's consider system of differential equations
$ t'=k n, $ $ n'=-k t-l b, $ $ b'=ln $ with unknow functions $t,n,b: I\rightarrow \mathbb R^3$.
How to show that scalar products below are zero: $ t\cdot t'=0, $ $ n\cdot n'=0, $ $ b\cdot b'=0. $
Thanks