Two particles A and B, move with constant velocities `vec(v_(1))" and "vec(v_(2))`. At the initial moment their position vectors are `vec(r_(1))" and "vec(r_(2))` respectively. The condition for particle A and B for their collision is

Options

A. `vecr_1 .vecv_1 = vecr_2 .vecv_2`
B. `vecr_1 xxvecv_1 = vecr_2 xxvecv_2`
C. `vecr_1 -vecr_2 = vecv_1 -vecv_2`
D. `(vecr_1-vecr_2)/(|vecr_1-vecr_2|)=(vecv_2-vecv_1)/(|vecv_2-vecv_1|)`

Answer

D

Explanation

`vecR = vecr_1 + vecv_1 t = vecr_2 + vecv_2 t`
`implies vecr_(1) -vecr_(2) = (vecv_2 -vecv_1) t`

So, `((r_1-r_2))/(|vecr_1-vecr_2|)=((v_2-v_1)t)/(|vecv_2-vecv_1|t)`
`implies (vecr_1-vecr_2)/(|vecr_1-vecr_2|)=(vecv_1-vecv_2)/(|vecv_1-vecv_2|)`