If the velocity of a rotating body of mass 50 kg is given by $\overrightarrow{\mathrm{V}}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ and radius vector $\overrightarrow{\mathrm{r}}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}},$ then its angular momentum is

Given,

$\overrightarrow{\mathrm{V}}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

$\overrightarrow{\mathrm{r}}=2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}},$

We know that angular momentum,

$\overrightarrow{\mathrm{L}}=\overrightarrow{\mathrm{r}}\times \overrightarrow{\mathrm{p}}=\mathrm{m}(\overrightarrow{\mathrm{r}}\times \overrightarrow{\mathrm{v}})$

$=50(2\hat{\mathrm{i}}\times (4\hat{\mathrm{j}}+5\hat{\mathrm{k}})+3\hat{\mathrm{j}}\times (3\hat{\mathrm{i}}+5\hat{\mathrm{k}}\left)\right)+4\hat{\mathrm{k}}\times (3\hat{\mathrm{i}}+4\hat{\mathrm{j}}))$

$=50(8\hat{\mathrm{k}}+10(-\hat{\mathrm{j}})+9(-\hat{\mathrm{k}})+15(\hat{\mathrm{i}})+12\hat{\mathrm{j}}+16(-\hat{\mathrm{i}}\left)\right)$

$=50(-\hat{\mathrm{i}}+2\hat{\mathrm{j}}-\hat{\mathrm{k}})=-50\hat{\mathrm{i}}+100\hat{\mathrm{j}}-50\hat{\mathrm{k}}$

Hence the correct answer is $\mathbf{-}\mathbf{50}\hat{\mathbf{i}}\mathbf{+}\mathbf{100}\hat{\mathbf{j}}\mathbf{-}\mathbf{50}\hat{\mathbf{k}}\mathbf{.}$