Two particles $$P_1$$ and $$P_2$$ move towards origin $$O$$, along the $$X$$ and $$Y$$ axes at constant speeds $$u_1$$ and $$u_2$$ respectively as shown in the figure. At $$t=0$$, the particles $$P_1$$ and $$P_2$$ are at distances $$a$$ and $$b$$ respectively from $$O$$. Then the instantaneous distance $$s$$ between the two particles is given by the relation

A

$$s=\left[a^2+b^2+(u_1^2+u_2^2)t^2-2t(au_1+bu_2)\right]^{1/2}$$

B

$$s=\left[a^2+b^2+(u_1^2+u_2^2)t^2-2t(bu_1+au_2)\right]^{1/2}$$

C

$$s=\left[a^2+b^2+(u_1^2+u_2^2)t^2+2t(au_1+bu_2)\right]^{1/2}$$

D

$$s=\left[a^2-b^2+(u_1^2+u_2^2)t^2-2t(au_1+bu_2)\right]^{1/2}$$