A particle of mass \(m\) is moving along the 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 statement is false for the angular momentum \(\vec L\) about the origin ?

1. A \(\;\left( a \right)\overrightarrow {\;L} \) \( = mv\left[ {\frac{R}{{\sqrt 2 }} + a} \right]\hat k\) ,when the particle is moving from \(B\) to \(C\)
2. B \(\vec L\) \( = \frac{{mv}}{{\sqrt 2 }}\;R\;\hat k\) , when the particle is moving from \(D\) to \(A\)
3. C \(\left( d \right)\overrightarrow {\;L} \) \( = mv\left[ {\frac{R}{{\sqrt 2 }} - a} \right]\hat k\) ,when the particle is moving from \(C\) to \(D\)
4. D Both (b) and (c)