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. `vecr_(1)-vecr_(2)=vecv_(1)-vecv_(2)`
B. `(vecr_(1)-vecr_(2))/(|vecr_(1)-vecr_(2)|)=(vecv_(2)-vecv_(1))/(|vec_(2)-vecv_(1)|)`
C. `vecr_(1)*vecv_(1)=vecr_(2)*vecv_(2)`
D. `vecr_(1)xxvecv_(1)=vecr_(2)xxvecv_(2)`

Answer

B

Explanation

`vecR=vecr_(1)+vecv_(1)t=vecr_(2)+vecv_(2)t`
`vecr_(1)-vecr_(2)=(vecv_(2)-vecv_(1))t`
`(vecr_(1)-vecr_(2))/(|vecr_(1)-vecr_(2)|)=((vecv_(2)-vecv_(1))t)/(|vecv_(2)-vecv_(1)|t)`
`(vecr_(1)-vecr_(2))/(|vecr_(1)-vecr_(2)|)=(vecv_(2)-vecv_(1))/(|vecv_(2)-vecv_(1)|)`