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 particle A and B for their collision is :
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) $\vec{r}_1 \times \vec{v}_1 = \vec{r}_2 \times \vec{v}_2$
Explanation
[Solution] They collide if the velocity of B relative to A points along the line from B to A, i.e. the unit vectors of $\vec{r}_1 - \vec{r}_2$ and $\vec{v}_2 - \vec{v}_1$ are equal. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.