The moment axis, force, and the perpendicular distance in the moment of the force calculation lie in two planes perpendicular to each other.

Explanation:

The moment of a force is a measure of its tendency to cause rotation about a specific point or axis. It is calculated by multiplying the magnitude of the force by the perpendicular distance from the point or axis to the line of action of the force. In order to understand why the moment axis, force, and the perpendicular distance lie in two planes perpendicular to each other, let's break down the components involved in the moment calculation.

1. Moment Axis:
The moment axis is the point or line about which the rotation occurs. It is represented by a point or a line in space. For example, if we consider a simple case of a force acting on a rigid body, the moment axis could be a fixed point on the body or an axis passing through the body. The moment axis can be any point or line in space.

2. Force:
The force is an external influence applied to the body that tends to cause a change in its state of motion. It is represented by a vector quantity with magnitude and direction. The force can act in any direction in space.

3. Perpendicular Distance:
The perpendicular distance is the shortest distance between the moment axis and the line of action of the force. It is a scalar quantity and represents the lever arm or moment arm. The perpendicular distance can be measured in any direction perpendicular to the line of action of the force.

Now, let's consider the moment calculation. The moment is given by the formula:

Moment = Force x Perpendicular Distance

When we calculate the moment, we multiply the magnitude of the force by the perpendicular distance. The force and the perpendicular distance are both vectors, and their product is a vector quantity. This vector quantity lies along the line of action of the force. Therefore, the moment axis, force, and the perpendicular distance lie in the same plane defined by the line of action of the force.

However, the moment can be positive or negative depending on the direction of rotation. The positive direction of rotation is determined by the right-hand rule. This means that the moment axis, force, and the perpendicular distance can lie in two planes perpendicular to each other, depending on the direction of rotation.

In conclusion, the moment axis, force, and the perpendicular distance in the moment of the force calculation lie in two planes perpendicular to each other. This is because the moment is a vector quantity and its direction is determined by the right-hand rule, resulting in two possible planes of rotation.