The time dependence of the position of a particle of mass \(m = 2\) is given by \(\vec r\,(t)\, = \,2t\,\hat i\, - 3{t^2}\hat j\) Its angular momentum with respect to the origin at time \(t = 2\) is

\(At\,t = 2\)

\(\overrightarrow v  = 2\hat i - 12\hat j\)

\(\overrightarrow p  = m\overrightarrow v  = 4i - 24\hat j\)

\(At\,t = 2\)

\(\overrightarrow r  = 4\hat i - 12\hat j\)

\(\overrightarrow L  = \overrightarrow r  \times \overrightarrow p  = \left| \begin{array}{l}
\hat i\,\,\,\,\,\,\,\,\,\,\hat j\,\,\,\,\,\,\,\,\,\,\,\hat k\\
4\,\,\,\,\,\, - 12\,\,\,\,\,\,\,\,\,0\\
4\,\,\,\,\,\, - 24\,\,\,\,\,\,\,\,\,0
\end{array} \right|\)

\( = \left\{ {4\left( { - 24} \right) + 4 \times 12} \right\}\hat k\)

\( = \left( { - 96 + 48} \right)\hat k\)

\( = \left(  -  \right)48\,\hat k\)