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Physics-

General

Easy

Question

Two particles 1 and 2 simultaneously leave two points O and A separated by a distance r, with velocities $stack v subscript 1 end subscript with minus on top$ and $stack v subscript 2 end subscript with minus on top$ respectively as shown in the figure. The smallest distance between the two particles

$\frac{l (v_{2} s i n b - v_{1} s i n a)}{\sqrt{v_{1}^{2} + v_{2}^{2} + 2 v_{1} v_{2} c o s (a + b)}}$
$\frac{l (v_{2} s i n b + v_{1} s i n a)}{\sqrt{v_{1}^{2} + v_{2}^{2} + 2 v_{1} v_{2} c o s (a + b)}}$
$\frac{l (v_{1} s i n b - v_{2} s i n a)}{\sqrt{v_{1}^{2} + v_{2}^{2} + 2 v_{1} v_{2} c o s (a + b)}}$
$\frac{l (v_{2} c o s b - v_{1} c o s a)}{\sqrt{v_{1}^{2} + v_{2}^{2} + 2 v_{1} v_{2} c o s (a + b)}}$

The correct answer is: $fraction numerator l open parentheses v subscript 2 end subscript s i n invisible function application b minus v subscript 1 end subscript s i n invisible function application a close parentheses over denominator square root of v subscript 1 end subscript superscript 2 end superscript plus v subscript 2 end subscript superscript 2 end superscript plus 2 v subscript 1 end subscript v subscript 2 end subscript c o s invisible function application left parenthesis a plus b right parenthesis end root end fraction$

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