ABC is triangle, right angled at A. The resultant of the force acting along $\overrightarrow{AB}, \overrightarrow{AC}$ with magnitudes $\frac{1}{AB}$ and $\frac{1}{AC}$ respectively is the force along $\overrightarrow{AD}$, where $D$ is the foot of the perpendicular from $A$ onto $BC$. The magnitude of the resultant is :

Question

( A ) $\frac{(AB)(AC)}{AB + AC}$
( B ) $\frac{1}{AD}$
( C ) $\frac{1}{AB} + \frac{1}{AC}$
( D ) $\frac{AB^2+AC^2}{(AB)^2 (AC)^2}$