For AI agents: use /llms.txt for the Nakafa content index.
The graphical method helps us see the resultant direction, but its accuracy depends on the drawing. The analytical method is more precise because it uses component calculations.
The method is to resolve every vector into the and axes, add the components along each axis, and then rebuild the resultant.
In the analytical method, vectors are added axis by axis, not directly from their arrow lengths.
Suppose several forces , , and act on an object. Each force is first split into horizontal and vertical components.
After all components are known, the resultant components are:
The resultant magnitude is:
The direction of the resultant relative to the positive axis can be found from:
If or is negative, identify the quadrant first so the direction is not misplaced.
A person walks in two stages. The first stage is equivalent to east and north. The second stage is equivalent to east and north.
| Displacement vector | component | component |
|---|---|---|
The resultant components are:
The total displacement magnitude is:
The resultant direction is:
Therefore above east. The total displacement is at north of east.
Vector subtraction is also done component by component. If , then:
For example, let and .
The negative sign in means the resulting component points downward.
So subtraction does not need a new rule. Keep the same axes, subtract matching components, then read the signs to recover the direction of the result.
