A.A=|A|^2 =constant

==> A.(dA/dt)+(dA/dt .A)=0

==> A.(dA/dt)=0

==> A is perpendicular to dA/dt

==> A.(dA/dt)+(dA/dt .A)=0

==> A.(dA/dt)=0

==> A is perpendicular to dA/dt