We know that the position vector in physics is defined as:

r(t) = x(t)i +y(t)j +z(t)k ,wherei=(1,0,0) ,j=(0,1,0) andk=(0,0,1).

Prove that :

$\displaystyle \frac{dr(t)}{dt} = \frac{dx(t)}{dt}$i+$\displaystyle \frac{dy(t)}{dt}$j+$\displaystyle \frac{dz(t)}{dt}$k