question_answer

If \[\overrightarrow{p},\] \[\overrightarrow{q}\] and \[\overrightarrow{r}\] are perpendicular to \[\overrightarrow{q}+\overrightarrow{r},\] \[\overrightarrow{r}+\overrightarrow{p}\] and \[\overrightarrow{p}+\overrightarrow{q},\] respectively and if \[|\overrightarrow{p}+\overrightarrow{q}|\,\,=6,\] \[|\overrightarrow{q}+\overrightarrow{r}|\,\,=4\sqrt{3}\,\]and \[|\overrightarrow{r}+\overrightarrow{p}|\,\,=4\] then \[|\overrightarrow{p}+\overrightarrow{q}+\overrightarrow{r}|\]is _________.

A)  10                               

B)  15

C)  \[5\sqrt{2}\]

D)  \[5\sqrt{5}\]

E)  None of these