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Two particles 1 and 2, move with constant velocities v1and v2.At initial moment their radius vectors are equal to r1 and r2.How must thes particles may be interrelated for the particles to collide?
r1+v1t=r2+v2t, t=(r1-r2)/(v2-v1), t which is a scalar, is a quotient of two vectors. this can be possible only if the two vectors are scalar multiples of each other. so r1-r2=k(v2-v1), where k is a scalar with appropriate dimensions. this implies that
r1-r2 and v2-v1 lie along the same line
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