# Force Vectors

By Ron Kurtus

A * force vector* is a representation of a force that has both magnitude and direction. This is opposed to simply giving the magnitude of the force, which is called a scalar quantity.

A vector is typically represented by an arrow in the direction of the force and with a length proportional to the force’s magnitude.

A major feature of force vectors is that they can be broken into components, according to the application of the force. Vector components are usually perpendicular to each other, although they also can be in a parallelogram configuration.

You can also add vectors to create a new vector.

Questions you may have include:

- How do you designate a force as a vector?
- What are the perpendicular vector components?
- What are the parallelogram vector components?
- How can you add two vectors?

This lesson will answer those questions. Useful tool: Units Conversion

## Designating force as a vector

Although you can designate a force simply as a number or scalar quantity, it is more useful to state it as a vector where you include the direction of the force.

Instead of saying that the force is 2 newtons, you would say something like the force is 2 newtons toward the ground.

## Perpendicular vector components

It is often useful to break a force vector into its components. An advantage of using perpendicular vector components is that you can use the Pythagorean Theory (**a ^{2} + b^{2} = c^{2})** to determine the lengths of the components.

Perpendicular vector components

## Parallelogram vector components

Sometimes the force vector is broken into parallelogram vector components.

Parallelogram vector components

## Force as sum of vectors

You can add two or more force vectors that are at angles with respect to each other to create a new force vector.

An example is if a force is moving an object in a given direction and wind applies a force on it at an angle, the new motion will be as if a force was applied in that direction.

Adding two force vectors

## Summary

A force vector is a representation that has both magnitude and direction. Such a vector is typically represented by an arrow in the direction of the force and with a length proportional to the force’s magnitude.

A major feature of force vectors is that they can be broken into components, according to the application of the force. You can also add vectors to create a new vector.

Listen and observe

## Resources and references

### Websites

**Vectors - Motion and Forces in Two Dimensions** - The Physics Classroom

**Basic Vector Operations** - Hyperphysics

**Vector Basics** - Physics4Kids.com

**Vector Physics** - Encyclopaedia Britannica

**Forces** - Physics Hyperbook

### Books

(Notice: The *School for Champions* may earn commissions from book purchases)

**Top-rated books on Physics of Force**

## Students and researchers

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**www.school-for-champions.com/science/
force_vectors.htm**

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## Where are you now?

## Force Vectors