Let $\overrightarrow{\mathrm{p}}=2\widehat{\mathrm{i}}+\widehat{\mathrm{j}}-2\widehat{\mathrm{k}},\mathrm{}\overrightarrow{\mathrm{q}}=\widehat{\mathrm{i}}+\widehat{\mathrm{j}}.$ If $\overrightarrow{\mathrm{r}}$ is a vector such that $\overrightarrow{\mathrm{p}}.\overrightarrow{\mathrm{r}}=\left|\overrightarrow{\mathrm{r}}\right|, \left|\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{p}}\right|=2\sqrt{2}$ and the angle between $\overrightarrow{\mathrm{p}}\times \overrightarrow{\mathrm{q}}$ and $\overrightarrow{\mathrm{r}}$ is $\frac{\mathrm{\pi }}{6}$, then the value of $\left|\left(\overrightarrow{\mathrm{p}}\times \overrightarrow{\mathrm{q}}\right)\times \overrightarrow{\mathrm{r}}\right|$ is equal to

• Correct answer
  A

  $\frac{3}{2}$
• B

  $\frac{1}{2}$
• C

  $\frac{3\sqrt{3}}{2}$
• D

  $3$

Hence, the correct answer is option: 'A'.