For the given vector $\vec{A} = 3\hat{i} - 4\hat{j} + 10\hat{k}$,the ratio of the magnitude of its component on the $x-y$ plane to the component on the $z$-axis is:

$A$ force of $5 \ N$ acts on a particle along a direction making an angle of $60^{\circ}$ with the vertical. Its vertical component will be $......... \ N$.

$A$ certain vector in the $xy$-plane has an $x$-component of $4 \,m$ and a $y$-component of $10 \,m$. It is then rotated in the $xy$-plane so that its $x$-component is doubled. Then its new $y$-component is (approximately) (in $\,m$)

The $Y$-component of velocity is $20$ and the $X$-component of velocity is $10$. The direction of motion of the body with the horizontal at this instant is

$A$ plane covers $500 \,m$ in a direction $60^o$ with the runway while starting the flight. Find the distance covered by the plane in the horizontal and vertical directions.

Add vectors $\vec{A}$,$\vec{B}$,and $\vec{C}$,each having a magnitude of $50 \text{ units}$ and inclined to the $X$-axis at angles $45^{\circ}$,$135^{\circ}$,and $315^{\circ}$ respectively.