Let the angle θ, 0<θ<(π)/2 between two unit vectors a and b be sin^-1((√ 65)/9). If the vector c =3 a +6 b +9( a × b ), then the value of 9( c · a…

Let the angle $\displaystyle \theta, 0<\theta<\frac{\pi}{2}$ between two unit vectors $\displaystyle \hat{a}$ and $\displaystyle \hat{b}$ be $\displaystyle \sin ^{-1}\left(\frac{\sqrt{65}}{9}\right)$. If the vector $\displaystyle \vec{c}=3 \hat{a}+6 \hat{b}+9(\hat{a} \times \hat{b})$, then the value of $\displaystyle 9(\vec{c} \cdot \hat{a})-3(\vec{c} \cdot \hat{b})$ is