Five equal forces of $10 \,N$ each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be ……….. $\mathrm{N}$

Two forces each numerically equal to $10$ $dynes$ are acting as shown in the adjoining figure, then the magnitude of resultant is………$dyne$

If $\overrightarrow A = 4\hat i – 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$ then magnitude and direction of $\overrightarrow A \, + \overrightarrow B $ will be

Two vectors $\overrightarrow{{X}}$ and $\overrightarrow{{Y}}$ have equal magnitude. The magnitude of $(\overrightarrow{{X}}-\overrightarrow{{Y}})$ is ${n}$ times the magnitude of $(\overrightarrow{{X}}+\overrightarrow{{Y}})$. The angle between $\overrightarrow{{X}}$ and $\overrightarrow{{Y}}$ is –

The ratio of maximum and minimum magnitudes of the resultant of two vector $\vec a$ and $\vec b$ is $3 : 1$. Now $| \vec a |$  is equal to