Question : Three particles start from the origin at the same time, one with a velocity 𝑣1 along 𝑥-axis, the second along the 𝑦-axis with a velocity 𝑣2 and the third along 𝑥 = 𝑦 line. The velocity of the third so that the three may always lie on the same line is
(A) \dfrac{v_{1}v_{2}}{v_{1}+v_{2}}
(B) \dfrac{\sqrt{2}v_{1}v_{2}}{v_{1}+v_{2}}
(C) \dfrac{\sqrt{3}v_{1}v_{2}}{v_{1}+v_{2}}
(D) zero
Answer : option (B)
Solution :
