$A$ man walks $20\,m$ at an angle $60^{\circ}$ north of east. How far towards the east has he travelled?

The velocity of a particle having a magnitude of $10 \ m/s$ in the direction of $60^{\circ}$ with the positive $X$-axis is:

Three vectors $\overrightarrow{OP}, \overrightarrow{OQ}$ and $\overrightarrow{OR}$ each of magnitude $A$ are acting as shown in the figure. The resultant of the three vectors is $A \sqrt{x}$. The value of $x$ is:

The $x$-component of the resultant of several vectors is:

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 ............

$A$ person pushes a box kept on a horizontal surface with a force of $100\,N$ as shown in the figure. In unit vector notation,the force $\vec{F}$ can be expressed as?