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Forces, vectors, and moments are related to the rotational tendency of a force, the magnitude and direction of a vector quantity, and the tendency of a force to rotate an object about a fixed axis.
Forces: The force of a spanner loosening a nut, a child on a seesaw, or a door opening around a hinge are all examples of forces.
Vectors: Vectors contain both magnitude and direction, and can describe the movement of an object from one point to another. For example, the vector formulation of the moment of force is the cross-product of the position and force vectors. The cross-product of two vectors results in a vector perpendicular to both vectors.
Moments: Moments, also called torques, are vector quantities that represent the tendency of a force to rotate a body about a fixed axis. The magnitude of a moment is the degree to which it will cause angular acceleration in the body. The direction of a moment is a scalar quantity corresponding to the direction of rotation. A moment that causes a counter-clockwise rotation is positive, and a moment that causes a clockwise rotation is negative.
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