ANS:A - sum of resolved parts in any two directions at right angles, are both zero

The principle you're referring to is part of the equilibrium conditions for an object subjected to forces. When forces act on an object, they can be resolved or broken down into components along different directions. The sum of these components can tell us about the balance of forces in those particular directions. Now, when we talk about the sum of resolved parts in any two directions at right angles being zero, we are essentially referring to the equilibrium of forces in those directions. This principle is based on Newton's first law, which states that an object will remain at rest or move with constant velocity unless acted upon by an unbalanced external force. Let's break it down further:

1. Resolved parts: When we resolve a force into its components, we are essentially breaking it down into its parts along specified directions. For instance, a force acting at an angle to the horizontal can be resolved into horizontal and vertical components.
2. At right angles: In many cases, we resolve forces into components along perpendicular directions. This is often the horizontal and vertical directions, but it could also be other mutually perpendicular axes.
3. Sum of resolved parts being zero: When we say the sum of resolved parts in any two directions at right angles is zero, it means that for any pair of perpendicular directions, the sum of the resolved components of all the forces acting in those directions equals zero. This signifies that the forces are balanced in those directions.

In mathematical terms, if we have forces acting in the horizontal (x) and vertical (y) directions, the equilibrium condition can be expressed as: ∑ Fx ​= 0 ∑ Fy​ = 0 This means that the sum of all the forces in the horizontal direction and the sum of all the forces in the vertical direction must individually add up to zero for the object to be in equilibrium. In summary, the principle of the sum of resolved parts in any two directions at right angles being zero is a statement of equilibrium, indicating that the forces are balanced in each perpendicular direction.