Suppose $f : \mathbb { R } \mapsto \mathbb { R } ^ { n }$ be a differentiable mapping satisfying $\| f ( t ) \| = 1$ for all $t \in \mathbb { R }$. Show that $\left\langle f ^ { \prime } ( t ) , f ( t ) \right\rangle = 0$ for all $t \in \mathbb { R }$. (Here $\|$.$\|$ denotes standard norm or length of a vector in $\mathbb { R } ^ { n }$, and $\langle . , .\rangle$ denotes the standard inner product (or scalar product) in $\mathbb { R } ^ { n }$.)