Let the angle \(\theta ,0 [JEE Main 2025, 7 Apr (Shift 1)]

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

[JEE Main 2025, 7 Apr (Shift 1)]