Which one of the following pairs cannot be the rectangular components of a force vector of $10 \, N$?

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.

The sum of three vectors is zero as shown in the figure. What will be the magnitudes of vectors $\vec{OB}$ and $\vec{OC}$?

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

The magnitude of vectors $\overrightarrow{ OA }, \overrightarrow{ OB }$ and $\overrightarrow{ OC }$ in the given figure are equal. The direction of $\overrightarrow{ OA }+\overrightarrow{ OB }-\overrightarrow{ OC }$ with the $x$-axis will be

$A$ 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.