Forces acting at some angle from the the coordinate axes can be resolved into mutually perpendicular forces called components. The component of a force parallel to the x-axis is called the x-component, parallel to y-axis the y-component, and so on.
Components of a Force in XY Plane
Given the slope of the line of action of the force as v/h (see figure to the right)
Components of a Force in 3D Space
Given the direction cosines of the force:
Given the coordinates of any two points along the line of action of the force (in reference to the figure shown, one of the points is the origin):
Let d = distance OB
Vector Notation of a Force (Also called Rectangular Representation of a Force)
Where λ is a unit vector. There are two cases in determining λ; by direction cosines and by the coordinates of any two points on the line of action of the force.
Given the direction cosines:
Given any two points P1(x1, y1) and P2(x2, y2) on the line of action of the force:
i, j, and k are unit vectors in the direction of x, y and z respectively.
Also note the following:
In simplest term
The above rectangular representation of a force is applicable in both 2D and 3D forces.