ans=   (v₂-v₁) .(p₁-p₂)                       here(  ) denote vectors

              [ mod(v₂-v₁)]²

 

 

 

 

 

soln: (v₂-v₁) vector is the relative velocit of 2 wrt 1

     shortest distance will b obtained at position where line joining 1 and 2 is perpendicular to the relative velocity vector

 

so let in time t the condition required is obtained,

let B be the angle between relative velocity vector and line joining 1&2

so cos (B)=mod(v₂-v₁)t/mod(p₁-p₂)=(v₂-v₁).(p₁-p₂₎/{mod[v2-v1]*mod[p1-p2]}