question_answer

If \[[\overset{\to }{\mathop{p}}\,+2\overset{\to }{\mathop{q}}\,+3\overset{\to }{\mathop{r}}\,\overset{\to }{\mathop{q}}\,+2\overset{\to }{\mathop{r}}\,+3\overset{\to }{\mathop{p}}\,\,\overset{\to }{\mathop{r}}\,+2\overset{\to }{\mathop{p}}\,+3\overset{\to }{\mathop{q}}\,]=54,\]where \[\overset{\to }{\mathop{p}}\,,\overset{\to }{\mathop{q}}\,\] and \[\overset{\to }{\mathop{r}}\,\] are three vectors then the value of\[\left| \begin{matrix}    \overset{\to }{\mathop{p}}\,.\overset{\to }{\mathop{p}}\, & \overset{\to }{\mathop{p}}\,.\overset{\to }{\mathop{q}}\, & \overset{\to }{\mathop{p}}\,.\overset{\to }{\mathop{r}}\,  \\    \overset{\to }{\mathop{p}}\,.\overset{\to }{\mathop{q}}\, & \overset{\to }{\mathop{q}}\,.\overset{\to }{\mathop{q}}\, & \overset{\to }{\mathop{q}}\,.\overset{\to }{\mathop{r}}\,  \\    \overset{\to }{\mathop{p}}\,.\overset{\to }{\mathop{r}}\, & \overset{\to }{\mathop{r}}\,.\overset{\to }{\mathop{q}}\, & \overset{\to }{\mathop{r}}\,.\overset{\to }{\mathop{r}}\,  \\ \end{matrix} \right|\] is

A)  4                                            

B)  9

C)  16                                         

D)  36