3particles start from a origin at the same time ,one with a velocity u1 along the x axis, 2nd along the y axis with a velocity u2 along the x=y line. The velocity of the third so that the 3 may always lie on the same line is?

Hi

Let us think on the situation after time t.

Particle 1 has reached pt ( u₁t , 0) and particle 2 is at (0, u₂t) . suppose the coordinates of particle 3 is (x,y)  and velocity u₃ . Nw apply the condition :

distance between paticle 3 and prticle 1 + distance between particle 3 and particle 2 = distance between particle 1 and particle 2 . Hence they ll be in the same line for all the time. Solve the equation by eliminating t, x and y .