$A$ force is applied at an angle of $60^\circ$ with the horizontal. If its horizontal component is $40 \ N$,then the vertical component is calculated to be ...... $N$.

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

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

The $Y$-component of velocity is $20$ and the $X$-component of velocity is $10$. The direction of motion of the body with the horizontal at this instant is