The angle made by the vector $\vec{A} = \hat{i} + \hat{j}$ with the $x$-axis is ....... $^\circ$.

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

What is the maximum number of components a vector can have when resolved in a plane?

$A$ displacement vector of magnitude $4$ makes an angle $30^{\circ}$ with the $x$-axis. Its rectangular components in the $x-y$ plane are .........

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

$A$ particle starting from the origin $(0, 0)$ moves in a straight line in the $(x, y)$ plane. Its coordinates at a later time are $(\sqrt{3}, 3)$. The path of the particle makes an angle of ......... $^o$ with the $x$-axis.