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

Two forces $\vec{F}_1$ and $\vec{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec{F}_1$ and $\vec{F}_2$ is $\cos^{-1}\left(\frac{1}{n}\right)$. The value of $|n|$ is . . . . . . .

$A$ particle undergoes three successive displacements given by $s_1 = \sqrt{2} \ m$ north-east,$s_2 = 2 \ m$ due south,and $s_3 = 4 \ m$ at $30^{\circ}$ north of west. The magnitude of the net displacement is:

The sum of the magnitudes of two forces acting at a point is $16 \,N$. If their resultant is normal to the smaller force and has a magnitude of $8 \,N$, then the forces are:

The magnitudes of vectors $\vec A, \vec B$ and $\vec C$ are $3, 4$ and $5$ units respectively. If $\vec A + \vec B = \vec C$,the angle between $\vec A$ and $\vec B$ is

The angle between two forces of equal magnitude $R$,if the magnitude of their resultant is $\frac{R}{2}$,is: