The component of a vector $\vec{r}$ along the $x$-axis will have a maximum value if

$A$ 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.

What is the maximum number of rectangular components into which a vector can be split in space?

$A$ vector $\overrightarrow{A}$ makes equal angles with the $x$,$y$,and $z$ axes. Find the magnitude of its components.

Consider a frame made up of two thin massless rods $AB$ and $AC$ as shown in the figure. $A$ vertical force $\overrightarrow{P}$ of magnitude $100 \; N$ is applied at point $A$ of the frame. Suppose the force $\overrightarrow{P}$ is resolved into components parallel to the arms $AB$ and $AC$ of the frame. The magnitude of the resolved component along the arm $AC$ is $x \; N$. The value of $x$,to the nearest integer,is ............

If the magnitude of a vector $\overrightarrow{p}$ is $25 \text{ units}$ and its $y$-component is $7 \text{ units}$, then its $x$-component is (in $\text{ units}$)