Gravitational field

See the us assume the v₁ is in positive and v₂ is in negative direction. or vice versa.
g wil act down ward so it will change the in both particles.
after time t
V_a= V₁ - gt
V_b= -V₂ - gt
now their velocity are perpendicular to each other.
dot product is zero
V_a.V_b= 0

(V₁ - gt).(-V₂ - gt)=0
solving t=√V₁V₂/g
the distance between then will be V_rel*t
= {V₁ - (-V₂)}√V₁V₂/g
putting the values of v1 and v2 respectively
we get d = 14√3 / g

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Please explain.

You have to use the concept that dot product of two perpendicular vectors is 0. assume that they will become perpendicular after time 't'. treat the point from where they are are projected be the origin. so,
(-v1i -gtj).(v2i - gtj) = 0
solve for t and then find the distance, you will get the answer.