109. If $A, B, C$ are the angles of a $\triangle A B C$, then

$$ \Delta=\left|\begin{array}{ccc} \sin 2 A & \sin C & \sin B \\ \sin C & \sin 2 B & \sin A \\ \sin B & \sin A & \sin 2 C \end{array}\right| \text { is equal to } $$

If $ A=\frac{1}{3}\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right] $ is an orthogonal matrix, then

Suppose $ p, q, r \neq 0 $ and system of equation $ (p+a) x+b y+c z=0 $, $ a x+(q+b) y+c z=0 $, $ a x+b y+(r+c) z=0 $, has a non-trivial solution, then the value of $ \frac{a}{p}+\frac{b}{q}+\frac{c}{r} $ is

If matrix $ A=\left[\begin{array}{ccc}3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1\end{array}\right] $ and $ A^{-1}=\frac{1}{k} \operatorname{adj}(A) $,