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

The component of vector $\overrightarrow{A}=a_x \hat{i}+a_y \hat{j}+a_z \hat{k}$ along the direction of $\hat{i}-\hat{j}$ is

The $X$ and $Y$ components of a force $F$ acting at $30^{\circ}$ to the $x$-axis are respectively:

$A$ 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 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.]

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