Two particles, 1 and 2, move with constant velocities `v_1` and `v_2`. At the initial moment their radius vectors are equal to `r_1` and `r_2`. How must these four vectors be interrelated for the particles to collide?

Options

A. `(r_(1)-r_(2))/(|r_(1)-r_(2)|)=(v_(2)-v_(1))/(|v_(2)-v_(1)|)`
B. `r_(2).v_(1)=r_(2).r_(2)`
C. `r_(1)xxv_(1)=r_(2)xxv_(2)`
D. `r_(1)xxv_(1)=v_(1)-v_(2)`

Answer

a

Explanation

For two particle A and B move with constant velocity `v_(1)`and `v_(2)` Such that two particle to collide, the direction of the velocity towards the relative position of the other particle
i.e `(r_(2)-r_(2))/(|r_(1)-r_(2)|)to`direction of relative position of 1w.r.t 2
Similarly,`(v_(1)-v_(2))/(|v_(1)-v_(2)|)to` direction of velocity of 2 w.r.t. 1 So, for collision of A and B we get
`(r_(1)-r_(2))/(|r_(1)-r_(2)|)=(v_(2)-v_(1))/(|v_(2)-v_(1)|)`
Alternate Method As resultant displacement of a particle

i.e `R=r_(1)-v_(1)t=r_(2)-v_(2)t`
`r_(1)-r_(2)=(v_(2)-v_(1))t`
`(r_(1)-r_(2))/(|r_(1)-r_(2)|)=(v_(2)-v_(1)t)/(|v_(2)-v_(1)|t)`
`(r_(1)-r_(2))/(|r_(1)-r_(2)|)=(v_(2)-v_(1))/(|v_(2)-v_(1)|)`