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

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 :

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