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A particle of mass \( m \) is moving along side of a square of side \( a \) , with a uniform speed \( v \) in the \( x-y \) plane as shown in the figure:

Which of the following statements is false for the angular momentum \( \vec{L} \) about the origin?
(1) \( \vec{L}=-\frac{m v}{\sqrt{2}} R \hat{k} \) when the particle is moving from \( A \) to \( B \)
(2) \( \vec{L}=m v\left[\frac{R}{\sqrt{2}}-a\right] \hat{k} \) when the particle is moving from \( C \) to \( D \).
(3) \( \vec{L}=m v\left[\frac{R}{\sqrt{2}}+a\right] \hat{k} \) when the particle is moving from \( B \) to \( C \).
(4) \( \vec{L}=\frac{m v}{\sqrt{2}} R \hat{k} \) when the particle is moving from \( D \) to \( A \).
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