# Determining quantities as vectors or not

• MathewsMD
This is not a purely arbitrary convention, but rather a mathematical fundamental as vectors have directions and magnitudes associated with them while scalars do not. In summary, current is a scalar quantity while current density is a vector quantity due to the dimensions of the vector and the fundamental characteristics of vectors and scalars.
MathewsMD
Why are some quantities vectors while others aren't? For example, we can calculate both current and current density, but why do we only consider current density to be a vector and current a scalar quantity? Is it a purely arbitrary convention or is it something more mathematically fundamental? I understand vectors like forces and displacement have directions and magnitudes associated with them, but I don't quite understand why we don't do the same thing for quantities like current? Is it to simplify equations only?

Current is a vector. The difference between current and current density is the dimensions of the vector. Current density is current per cross sectional area, or number of charges moving through a volume, while current is descriptive of charges moving along a line.

## 1. What is the difference between a vector and a non-vector quantity?

A vector quantity has both magnitude and direction, while a non-vector quantity only has magnitude. This means that a vector quantity can be represented by a direction and a length, while a non-vector quantity can only be represented by a numerical value.

## 2. How do you determine if a quantity is a vector or not?

A quantity is considered a vector if it has both magnitude and direction. This can be determined by looking at the physical properties of the quantity and determining if it has a direction associated with it. For example, velocity is a vector quantity because it has both magnitude (speed) and direction (direction of motion).

## 3. Can a quantity be both a vector and a non-vector?

No, a quantity can only be one or the other. If a physical quantity has both magnitude and direction, it is considered a vector. If it only has magnitude, it is a non-vector quantity.

## 4. How are vectors represented mathematically?

Vectors are represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude of the vector. In mathematical notation, vectors are typically denoted by boldface letters or with an arrow above the letter.

## 5. Why is it important to distinguish between vector and non-vector quantities?

It is important to distinguish between vector and non-vector quantities because they behave differently in mathematical equations and physical situations. For example, adding two vectors together requires taking into account both magnitude and direction, while adding two non-vector quantities only involves simple addition of their numerical values. Additionally, understanding whether a quantity is a vector or not can help in accurately representing and solving physical problems.

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