System of Forces

Q. Two forces A and B are acting at an angle $\theta$. Their resultant 'R' will make an angle $\alpha$ with the force B, such that sin $\alpha$ is equal to

1. $\frac{A+Bsin\theta }{\sqrt{A^2+B^2-2ABcos\theta }}$
2. $\frac{Bsin\theta }{\sqrt{A^2+B^2+2ABcos\theta }}$
3. $\frac{Asin\theta }{\sqrt{A^2+B^2+2ABcos\theta }}$
4. $\frac{Bcos\theta }{\sqrt{A^2+B^2-2ABcos\theta }}$

Q. If a number of forces act on a rigid body, each force may be replaced by an equal parallel force acting through a fixed point, together with a couple. For the rigid body to be in equilibrium.

1. Both resultant force and couple must be zero
2. The resultant couple on the body must be zero
3. The resultant force at the fixed point must be zero
4. None of the above need be zero

Q.

What should be the total vertical force in system when body is in equilibrium?