A mosquito is moving with a velocity \(\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s\) and accelerating in uniform conditions. What will be the direction of mosquito after \(2 \,s\) ?

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

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

\(\therefore\) 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.