\(At\,t = 2\)
\(\overrightarrow v = 2\hat i - 12\hat j\)
\(\overrightarrow p = m\overrightarrow v = 4i - 24\hat j\)
\(At\,t = 2\)
\(\overrightarrow r = 4\hat i - 12\hat j\)
\(\overrightarrow L = \overrightarrow r \times \overrightarrow p = \left| \begin{array}{l}
\hat i\,\,\,\,\,\,\,\,\,\,\hat j\,\,\,\,\,\,\,\,\,\,\,\hat k\\
4\,\,\,\,\,\, - 12\,\,\,\,\,\,\,\,\,0\\
4\,\,\,\,\,\, - 24\,\,\,\,\,\,\,\,\,0
\end{array} \right|\)
\( = \left\{ {4\left( { - 24} \right) + 4 \times 12} \right\}\hat k\)
\( = \left( { - 96 + 48} \right)\hat k\)
\( = \left( - \right)48\,\hat k\)