Final answer:
The algebraic sum of the resolved part of forces in a given direction is equal to the resolved part of their resultant in the same direction.
Step-by-step explanation:
To show that the algebraic sum of the resolved part of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction, we need to understand the concept of vector addition and component resolution.
Consider two forces applied in the same direction. The resultant force is the sum of these two forces in that direction. When forces are applied in opposite directions, the resultant force is still the sum of the applied forces, taking into account the positive and negative directions chosen.
This concept is illustrated by examples and can be analyzed using graphical methods or analytical methods, such as finding vector components and using vector algebra to find the sum of vectors.