Given :
$\overrightarrow{v}=0.5t^2\hat{\mathrm{i}}+3t\hat{\mathrm{j}}+9\hat{\mathrm{k}}$

${\overrightarrow{v}}_{\mathrm{at} t=2}=2\hat{\mathrm{i}}+6\hat{\mathrm{j}}+9\hat{\mathrm{k}}$

$\therefore$ Angle made by direction of motion of mosquito will be,

${\cos }^{-1}\frac{2}{11}$ (from $x$-axis) $={\tan }^{-1}\frac{\sqrt{117}}{2}$

${\cos }^{-1}\frac{6}{11}$ (from $y$-axis) $={\tan }^{-1}\frac{\sqrt{85}}{6}$

${\cos }^{-1}\frac{9}{11}$ (from $z$-axis) $={\tan }^{-1}\frac{\sqrt{40}}{9}$