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

Vector $P = 6 \hat{i} + 4 \sqrt{2} \hat{j} + 4 \sqrt{2} \hat{k}$ makes an angle with the $z$-axis equal to:

$A$ 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?

The $x$-component of the resultant of several vectors is:
$(a)$ equal to the sum of the $x$-components of the individual vectors.
$(b)$ less than the sum of the magnitudes of the individual vectors.
$(c)$ greater than the sum of the magnitudes of the individual vectors.
$(d)$ equal to the sum of the magnitudes of the individual vectors.

Consider an object kept at the centre, in the $XY$-plane, on which five coplanar forces act as shown in the figure. The resultant force on the object is

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