Let \[\overset{\to }{\mathop{a}}\,,\text{ }\overset{\to }{\mathop{b}}\,\] and \[\overset{\to }{\mathop{c}}\,\] be three non-coplanar vectors, and let \[\overset{\to }{\mathop{p}}\,,\text{ }\overset{\to }{\mathop{q}}\,\] and \[\overset{\to }{\mathop{r}}\,\] be the vectors defined by the relations \[\overset{\to }{\mathop{p}}\,=\frac{\overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\,}{[\overset{\to }{\mathop{a}}\,\,\overset{\to }{\mathop{b}}\,\,\overset{\to }{\mathop{c}}\,]},\overset{\to }{\mathop{q}}\,=\frac{\overset{\to }{\mathop{c}}\,\times \overset{\to }{\mathop{a}}\,}{[\overset{\to }{\mathop{a}}\,\,\overset{\to }{\mathop{b}}\,\,\overset{\to }{\mathop{c}}\,]}\] and \[\overset{\to }{\mathop{r}}\,=\frac{\overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\,}{[\overset{\to }{\mathop{a}}\,\,\overset{\to }{\mathop{b}}\,\,\overset{\to }{\mathop{c}}\,]}.\] Then the value of the expression \[(\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,).\overset{\to }{\mathop{p}}\,+(\overset{\to }{\mathop{b}}\,+\overset{\to }{\mathop{c}}\,).\overset{\to }{\mathop{q}}\,+(\overset{\to }{\mathop{c}}\,+\overset{\to }{\mathop{a}}\,).\overset{\to }{\mathop{r}}\,\] is equal to

• A. 0
• B. 1
• C. 2
• D. 3