Derivative of a vector function of a constant length

Let v(t) be a vector function whose norm is constant, say, |v(t)|=c.
Then
|v|^2=v.v=c^2,and
(v.v)'=v'v+vv'=2v.v'=c'=0 by differentiation.
This yields the following Result.
The derivative of a vector v(t) of constant norm is either zero vector or is perpendicular to v(t).
Since Dot product of two nonzero vectors are zero iff they are perpendicular to each other.
[Erwin Kreyszig, Advanced Engineering Mathematics 8th eddition. Page 426.]