A particle of mass \( m \) moves in the XY plane with a velocity \(...

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A particle of mass \( m \) moves in the XY plane with a velocity \( \mathrm{V} \) along the straight line \( \mathrm{AB} \). If the angular momentum of the particle about the origin \( \mathrm{O} \) is \( \mathrm{L}_{\mathrm{A}} \) when it is at \( \mathrm{A} \) and \( L_{B} \) when it is at \( B \), then:
(1) \( \mathrm{L}_{\mathrm{A}}\mathrm{L}_{\mathrm{B}} \)
(2) \( \mathrm{L}_{\mathrm{A}}=\mathrm{L}_{\mathrm{B}} \)
(3) The relationship between \( \mathrm{L}_{\mathrm{A}} \) and \( \mathrm{L}_{B} \) depends upon the slope of the line \( \mathrm{AB} \)
(4) \( \mathrm{L}_{\mathrm{A}}\mathrm{L}_{\mathrm{B}} \)
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