Two particles A and B, move with constant velocities vecv1 and vecv2. At the initial moment their position vectors are vecr1, and vecr2 respectively. The condition for particles A and B for their collision is

Question

Two particles A and B, move with constant velocities vecv1 and vecv2. At the initial moment their position vectors are vecr1, and vecr2 respectively. The condition for particles A and B for their collision is (A)  vecr1 × vecv1= vecr2 × vecv2 (B)  vecr1 - vecr2= vecv1 × vecv2 (C) ( vecr1- vecr2/| vecr1- vecr2|)=( vecv1- vecv2/| vecv1- vecv2|) (D)  vecr1 ⋅ vecv1= vecr2 ⋅ vecv2

Tardigrade Admin · Accepted Answer

Q. Two particles $A$ and $B$ , move with constant velocities $v_{1}$ and $v_{2}$ . At the initial moment their position vectors are $r_{1}$ , and $r_{2}$ respectively.
The condition for particles $A$ and $B$ for their collision is

$r_{1} \times v_{1} = r_{2} \times v_{2}$

$r_{1} - r_{2} = v_{1} \times v_{2}$

$\frac{r _{1} - r _{2}}{∣ r _{1} - r _{2} ∣} = \frac{v _{1} - v _{2}}{∣ v _{1} - v _{2} ∣}$

$r_{1} \cdot v_{1} = r_{2} \cdot v_{2}$

Q. Two particles A and B, move with constant velocities v1​​ and v2​​. At the initial moment their position vectors are r1​​, and r2​​ respectively. The condition for particles A and B for their collision is

r1​​×v1​​=r2​​×v2​​

r1​​−r2​​=v1​​×v2​​

∣r1​​−r2​​∣r1​​−r2​​​=∣v1​​−v2​​∣v1​​−v2​​​

r1​​⋅v1​​=r2​​⋅v2​​

Q. Two particles $A$ and $B$ , move with constant velocities $v_{1}$ and $v_{2}$ . At the initial moment their position vectors are $r_{1}$ , and $r_{2}$ respectively.
The condition for particles $A$ and $B$ for their collision is

$r_{1} \times v_{1} = r_{2} \times v_{2}$

$r_{1} - r_{2} = v_{1} \times v_{2}$

$\frac{r _{1} - r _{2}}{∣ r _{1} - r _{2} ∣} = \frac{v _{1} - v _{2}}{∣ v _{1} - v _{2} ∣}$

$r_{1} \cdot v_{1} = r_{2} \cdot v_{2}$