Mathematics - Vector Question with Solution | TestHub

(P) The centroid-edge determinant is the tetrahedron determinant divided by $3^3$, giving $V=9$. (Q) Reflection in the plane gives $3(a-b+c)=8$. (R) Projection on the line gives $k=27$, hence $k/9=3$. (S) Unit volume gives $|[\vec{a}\vec{b}\vec{c}]|=6$, so $\sqrt{3}\cdot 2\cdot \sqrt{6}\sin \theta =6$, hence $\sin \theta =1/\sqrt{2}$. With negative dot product, $\theta =3\pi /4$, so $p+q=7$.