What is the minimum number of coplanar vectors having different magnitudes that can be added to give a zero resultant?

If $\overrightarrow{R}$ is the resultant vector of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$,then $|\overrightarrow{R}|$ is . . . . . . $|\overrightarrow{A}| + |\overrightarrow{B}|$.

What displacement must be added to the displacement $25\hat{i} - 6\hat{j} \text{ m}$ to give a resultant displacement of $7.0 \text{ m}$ pointing in the $X$-direction?

Two forces of magnitude $F$ have a resultant of the same magnitude $F$. The angle between the two forces is ........ $^o$

At what angle must the two forces $(x + y)$ and $(x - y)$ act so that the resultant may be $\sqrt{x^2 + y^2}$?

Two vectors having equal magnitudes of $x$ units acting at an angle of $45^\circ$ have a resultant of $\sqrt{2 + \sqrt{2}}$ units. The value of $x$ is