$A$ 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 statements is false for the angular momentum $\vec L$ about the origin?

• A
  $\vec L = mv\left[ {\frac{R}{{\sqrt 2 }} + a} \right]\hat k$,when the particle is moving from $B$ to $C$
• B
  $\vec L = \frac{{mvR}}{{\sqrt 2 }}\hat k$,when the particle is moving from $D$ to $A$
• C
  $\vec L = mv\left[ {\frac{R}{{\sqrt 2 }} - a} \right]\hat k$,when the particle is moving from $C$ to $D$
• D
  Both $(b)$ and $(c)$