Motion in a Plane

Given, velocity of mosquito,
v=(0.5t2

∧

i

+3t

∧

j

+9

∧

k

)‌m∕s
At t=2s,v=0.5(2)2

∧

i

+3(2)

∧

j

+9

∧

k

=2

∧

i

+6

∧

j

+9

∧

k

∴ Angle along X-axis,
cos‌α=‌

2

√22+62+92

=‌

2

√121

=‌

2

11

or α=cos−1(‌

2

11

)
Similarly, angle along Y-axis, cos‌β=‌

6

11

⇒‌‌β=cos−1(‌

6

11

)
Angle along Z-axis, cos‌γ=‌

9

11

⇒‌‌γ=cos−1(‌

9

11

)
∴ Angle made by the direction of motion of mosquito will be
cos−1(‌

2

11

) from X-axis =tan−1‌

√117

2

cos−1(‌

6

11

) from Y-axis =tan−1‌

√85

2

cos−1(‌

9

11

) from Z-axis =tan−1(‌

√40

9

)