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 ……….. $\mathrm{N}$

If the angle between $\hat a$ and $\hat b$ is $60^o$, then which of the following  vector $(s)$ have magnitude one

$(A)$ $\frac{\hat a + \hat b}{\sqrt 3}$     $(B)$ $\hat a + \widehat b$     $(C)$ $\hat a$      $(D)$ $\hat b$

Magnitudes of two vector $\overrightarrow A $ and $\overrightarrow B $ are $4$ units and $3$ units respectively. If these vectors are $(i)$ in same direction $(\theta = 0^o).$ $(ii)$ in opposite direction $(\theta = 180^o)$, then give the magnitude of resultant vector.

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

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