Vector Notation and Components
Write vectors as ordered lists of coordinates.
Key idea
Write vectors as ordered lists of coordinates.
In depth
A vector in 2D is written (x, y) or as a column; its components give how far to go along each axis. In n dimensions, v = (v₁, ..., vₙ). The same vector can be drawn anywhere; only its length and direction matter.
Worked example
v = (3, −2) means 3 right and 2 down. In 3D, (1, 2, 3) has three components.
Formula
Real-world uses
- Describing a drone’s position in 3D
- Storing player positions in a game
Common mistake
Confusing a point with a vector; a point is a location, a vector is a displacement.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Vector Notation and Components?
Write vectors as ordered lists of coordinates. It is a topic at the intermediate level in Linear Algebra.
What is the formula for Vector Notation and Components?
The key formula is v = (v₁, v₂, v₃).
Where is Vector Notation and Components used in real life?
Real-world examples: Describing a drone’s position in 3D; Storing player positions in a game.
What should I learn before Vector Notation and Components?
Make sure you are comfortable with Scalars and Vectors, the previous topic in Linear Algebra.
What is a common mistake with Vector Notation and Components?
Confusing a point with a vector; a point is a location, a vector is a displacement.
How can I practise Vector Notation and Components?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Vector Notation and Components?
Move on to Vector Addition next.
Related intermediate topics in Linear Algebra
- Scalars and Vectors – A scalar is a number; a vector has magnitude and direction.
- Vector Addition – Add component-wise; geometrically tip-to-tail.
- Scalar Multiplication – Scale a vector’s length.
- Vector Magnitude – Length of a vector.
- Unit Vectors – Vectors of length 1, found by normalising.
- Matrices: Definition – A rectangular array of numbers with m rows and n columns.