Let \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,,\overset{\to }{\mathop{c}}\,\] be non-coplanar vectors and\[\overset{\to }{\mathop{p}}\,=\frac{\overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\,}{[\overset{\to }{\mathop{a}}\,\overset{\to }{\mathop{b}}\,\overset{\to }{\mathop{c}}\,]},\,\,\,\overset{\to }{\mathop{q}}\,=\frac{\overset{\to }{\mathop{c}}\,\times \overset{\to }{\mathop{a}}\,}{[\overset{\to }{\mathop{a}}\,\overset{\to }{\mathop{b}}\,\overset{\to }{\mathop{c}}\,]},\,\,\,\overset{\to }{\mathop{r}}\,=\frac{\overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\,}{[\overset{\to }{\mathop{a}}\,\overset{\to }{\mathop{b}}\,\overset{\to }{\mathop{c}}\,]}.\] What is the value of\[(\vec{a}-\vec{b}-\vec{c}).\vec{p}+(\vec{b}-\vec{c}-\vec{a}).\vec{q}+(\vec{c}-\vec{a}-\vec{b}).\vec{r}\]?

• A. 0
• B. -3
• C. 3
• D. -9