$A$ 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 $......... \ N$.

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

The resultant of these forces $\overrightarrow{OP}, \overrightarrow{OQ}, \overrightarrow{OR}, \overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately $\ldots \ldots \text{N}$.
[Take $\sqrt{3}=1.7, \sqrt{2}=1.4$. Given $\hat{i}$ and $\hat{j}$ are unit vectors along $x, y$ axes.]

Find the magnitude and direction of the vectors $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$. What are the components of a vector $\vec{A}=2\hat{i}+3\hat{j}$ along the directions of $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$?

Can the magnitude of the rectangular components of a vector be greater than the magnitude of the vector itself? Explain.

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