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 P_{1}(x_{1}, y_{1}) and P_{2}(x_{2}, y_{2}) on the line of action of the force:

Where**i**, **j**, and **k** are unit vectors in the direction of x, y and z respectively.

Note:

Also note the following:

Thus,

In simplest term

The above rectangular representation of a force is applicable in both 2D and 3D forces.

## Comments

## engineering mechanics

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## Re: Components of a Force

Hello,

Can you please check the formulas once again. I may be wrong, but there is some error in the Angle consideration.

Thanks for uploading, it was useful.