Many quantities in technology cannot be described fully without giving their **direction** as well as their **magnitude **(how large a quantity is relative to zero). For example, it is not always useful to know how fast something is moving (speed) without knowing the **direction** in which it is moving in.

**Velocity** is called a **vector quantity** because velocity gives you both *magnitude* and *direction*, as opposed to speed, which gives you only the magnitude – called a **scalar quantity**. Quantities that have magnitude but **no direction** are called *scalar quantities*. This includes time, volume, mass, and so on.

Apart from velocity, other vector quantities include *force* and *acceleration*. A vector is represented by an **arrow** whose length is **proportional** to the magnitude of the vector and whose direction is the same as the direction (i.e. in degrees or radians) of the vector quantity.

This unit will introduce how to add individual vectors to produce a single vector, known as a **resultant vector**. Resultant vectors can also be broken down into *component vectors* using trigonometric functions and the Pythagorean theorem. **Resolving a vector **means to replace it by its *components* (more on this next section).

Before you can learn that, you need to recognize how vectors are communicated on paper. Vectors are represented differently in different textbooks, but they are usually written in **boldface type**. The most common notation used in textbooks have the following characteristics:

- Boldface roman capitals,
- and non-boldface italic capitals to represent
**scalar quantities**.

For this lesson, **B** is understood to be a vector quantity*,* having both magnitude and direction, while *B* is understood to be a scalar quantity, having magnitude but no direction. Taking into account the vector arrow shown earlier, it can also be represented as:

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When written by hand, a *vector accent* (⇀) is added above the letters:

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Similarly, scalar quantities written by hand are surrounded by the *absolute symbol* (| |) or sometimes with double absolute values (|| ||) with a *vector accent*:

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You can specify a vector’s magnitude and direction by writing it in **polar form**. For example, to write a vector that has a length of 5 units and a direction of 38°:

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On a Cartesian plane, this would look like: