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QAIPM-2015-Ph-1271: NEET 2015 Physics - Class 11 AIPM-2015-Ph-1271 Solution: Two particles A and B move with constant velocities $ {v}_1$…

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

\vec{r}_1 \cdot \vec{v}_1 = \vec{r}_2 \cdot \vec{v}_2

\vec{r}_1 \times \vec{v}_1 = \vec{r}_2 \times \vec{v}_2

\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|}

\vec{r}_1 - \vec{r}_2 = \vec{v}_1 - \vec{v}_2

A ${\overrightarrow r _1} \times {\overrightarrow v _1} = {\overrightarrow r _2} \times {\overrightarrow v _2}$ r 1 _ _ v 1 _ = r 2 _ _ v 2 _
B ${\overrightarrow r _1} - {\overrightarrow r _2} = {\overrightarrow v _1} - {\overrightarrow v _2}$ r 1 _ _ r 2 _ = v 1 _ _ v 2 _
C ${{{{\overrightarrow r }_1} - {{\overrightarrow r }_2}} \over {\left| {{{\overrightarrow r }_1} - {{\overrightarrow r }_2}} \right|}} = {{{{\overrightarrow v }_2} - {{\overrightarrow v }_1}} \over {\left| {{{\overrightarrow v }_2} - {{\overrightarrow v }_1}} \right|}}$ _ r 1 _ _ r 2 _ _ r 1 _ _ r 2 _ _ = _ v 2 _ _ v 1 _ _ v 2 _ _ v 1 _ _
D ${\overrightarrow r _1}.{\overrightarrow v _1} = {\overrightarrow r _2}.{\overrightarrow v _2}$ r 1 _ . v 1 _ = r 2 _ . v 2 _

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