Mathematics - Vector Question with Solution | TestHub

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