Given :

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

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

$\therefore$ 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 $)=\tan ^{-1} \frac{\sqrt{40}}{9}$

None of the option is matching.

Hence this question should be bonus.