**Forces in Two Dimensions Facts**

Forces in a single dimension can be represented by a vector that is either perfectly vertical or horizontal, but a force in two dimensions must be drawn as a vector that is diagonal or at an angle. These two-dimensional diagonal vectors can be broken down into their component one-dimensional vectors. For example, a force vector that is pointed up and to the right can be broken into two simple vectors—one pointed upward and one pointed to the right. These compound vectors are used to describe two-dimensional forces around us such as a plane taking off or a ball traveling in an arc.

**Fun Facts**

- Very few forces actually exist purely in one dimension. Factoring in two or even three dimensions allows for a more accurate understanding of force and motion.
- Any two-dimensional force can be broken up into two component forces.
- These two component forces, when added together, make up a two-dimensional force vector.
- Component vectors cannot be added like ordinary numbers. Instead, they form the two short sides of a triangle—with the two-dimensional vector as the hypotenuse.
- Because of this triangular quality of two-dimensional forces, knowing information such as the angle, sine, cosine, or tangent of a vector can allow you to calculate the magnitude of a two-dimensional force using trigonometry.
- Forces, including those in two-dimensions, were studied and explained by Sir Isaac Newton in the seventeenth century.
- Physicists did not begin using component vectors to describe two-dimensional forces until the nineteenth century.
- Pushing an object up an inclined plane, rolling a ball down a hill, and throwing a dart at an angle are all examples of forces acting in two dimensions.

**Vocabulary **

- Vector: A quantity that has both magnitude and direction, represented as an arrow and used to depict force.
- Trigonometry: A branch of mathematics that deals with triangles, including the relationships between their sides, angles, and functions.

**Questions and Answers **

Question: Would a car driving up a hill be an example of force acting in one dimension or in two dimensions?

Answer: Two dimensions. To go up a hill the car must be enacting both horizontal and vertical component forces.

__Watch a video__ that will help you better understand forces in two dimensions.