Two forces,each numerically equal to $10$ $dyne$,are acting as shown in the adjoining figure. The magnitude of the resultant force is ......... $dyne$.

Two forces of $10 \,N$ and $6 \,N$ act upon a body. The directions of the forces are unknown. The resultant force on the body may be .........$N$.

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

Given that $A_1+A_2=5 A_3$ and $A_1-A_2=3 A_3$, where $A_3=2 \hat{i}+4 \hat{j}$, find the value of $\frac{|A_1|}{|A_2|}$.

The sum of two forces acting at a point is $16\, N.$ If the resultant force is $8\, N$ and its direction is perpendicular to the minimum force,then the forces are:

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $n$ times the magnitude of $(\vec A - \vec B)$. The angle between $\vec A$ and $\vec B$ is