You can write a vector using special notation or by listing its components.
Writing a vector involves using specific symbols or representing it through its components along coordinate axes. The method often depends on whether you are writing by hand or using a computer, and can vary by field of study.
Handwritten Notation
In handwriting, vectors are typically distinguished from scalar quantities (simple numbers) using specific marks above or below the letter representing the vector.
- Tilde: A tilde (~) placed above the letter (e.g., $\tilde{a}$).
- Arrow: An arrow (→) placed above the letter (e.g., $\vec{a}$).
- Underline: An underline (_) placed below the letter (e.g., $\underline{a}$).
These conventions for handwritten notation can vary with geography and subject area.
| Notation Example | Description | Where Used (Often) |
|---|---|---|
| $\vec{a}$ | Letter with arrow above | Physics, Engineering |
| $\tilde{a}$ | Letter with tilde above | Statistics, Pure Math |
| $\underline{a}$ | Letter with underline below | Some European texts, Physics |
Note: When typing, vectors are often represented using bold typeface (e.g., a) or an arrow above the letter (e.g., $\vec{a}$).
Writing Vectors Using Components
Another common way to write a vector is by describing its components along each of the axes in a coordinate system, such as Cartesian coordinates. This method specifies how far the vector extends in each direction.
- Components: These are the scalar values representing the projection of the vector onto each axis (e.g., the x, y, and z axes in 3D space).
- Representation: The components are typically listed in parentheses or brackets, separated by commas.
Example:
As stated in the reference, a vector can be described using Cartesian coordinates, giving the components of the vector along each of the axes.
- A 3D vector 'a' with components $a_1$, $a_2$, and $a_3$ along the x, y, and z axes, respectively, is written as:
a = (a1, a2, a3)
This component form provides a clear, numerical representation of the vector's magnitude and direction from the origin.
