A mosquito is moving with a velocity → v = 0 . 5 t ^ 2 ^ i + 3t ^ j...

Given :
\overset{\to}{v} = 0 . 5{t}^{2}\overset{^}{i} + 3t\overset{^}{j} + 9\overset{^}{k}

\overset{\to}{v}att = 2 = 2\overset{^}{i} + 6\overset{^}{j} + 9\overset{^}{k}

$∴$ Angle made by direction of motion of mosquito will be,

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

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

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