$A$ mass $M$ is suspended by a system of light inextensible strings as shown in the figure. Find the tension in the horizontal string.

The resultant of two forces,one double the other in magnitude,is perpendicular to the smaller of the two forces. The angle between the two forces is ........ $^o$

As shown in the figure,the two sides of a step ladder $BA$ and $CA$ are $1.6 \; m$ long and hinged at $A$. $A$ rope $DE$ of length $0.5 \; m$ is tied halfway up. $A$ weight of $40 \; kg$ is suspended from a point $F$,$1.2 \; m$ from $B$ along the ladder $BA$. Assuming the floor to be frictionless and neglecting the weight of the ladder,find the tension in the rope and the forces exerted by the floor on the ladder. (Take $g = 9.8 \; m/s^2$)

The sum of three forces $\vec F_1 = 100\,N$,$\vec F_2 = 80\,N$,and $\vec F_3 = 60\,N$ acting on a particle is zero. The angle between $\vec F_1$ and $\vec F_2$ is nearly .......... $^o$

$A$ mass $M$ is suspended by a rope from a rigid support at $A$ as shown in the figure. Another rope is tied at point $B$,and it is pulled horizontally with a force $F$. If the string $AB$ makes an angle $\theta$ with the vertical in equilibrium,then the tension in the string $AB$ is:

Three concurrent co-planar forces $1 \,N$,$2 \,N$,and $3 \,N$ acting along different directions on a body: