Q .     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 particles `A` and `B` for their collision is:

AIPMT 2015
A

`\vec{r_1} - \vec {r_2} = \vec {v_1} - \vec {v_2}`

B

`\frac{\vec {r_1} - \vec {r_2} }{ |\vec{r_1} - \vec {r_2} |} = \frac{\vec {v_2} - \vec {v_1} }{ |\vec {v_2} - \vec {v_1} |}`

C

`\vec {r_1} \cdot \vec {v_1} = \vec {r_2} \cdot \vec {v_2}`

D

`\vec {r_1} \times \vec {v_1} = \vec {r_2} \times \vec {v_2}`

HINT

For the collision the final position of the both particles should be equal. hence, `\vec{r_1}+\vec{v_1}t=\vec{r_2}+\vec{v_2}t`

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