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The position and the velocity of two particles are \(\vec{r}_1\), \(\vec{r}_2\) and \(\vec{v}_1\), \(\vec{v}_2\). Prove that they collide only if : \((\vec{r}_1 - \vec{r}_2) \times (\vec{v}_1 - \vec{v}_2) = 0\).

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The position and the velocity of two particles are \(\vec{r}_1\), \(\vec{r}_2\) and \(\vec{v}_1\), \(\vec{v}_2\). Prove that they collide only if : \((\vec{r}_1 - \vec{r}_2) \times (\vec{v}_1 - \vec{v}_2) = 0\).

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