Linear Algebra
Vectors
A simple introduction to vectors, their meaning, notation and basic operations.
What you’ll learn
Understand what a vector represents.
Read and write vectors in coordinate form.
Calculate vector magnitude.
Concept
What is a vector?
A vector is a mathematical object that has both magnitude and direction. In two dimensions, we often represent a vector using two numbers.
Vector notation
v = (3, 4)
Here, the vector moves 3 units horizontally and 4 units vertically.
Key idea
A vector tells us not only “how much,” but also “which way.”
Visual explanation
Worked example
Finding magnitude
Find the magnitude of the vector v = (3, 4).
|v| = √(3² + 4²)
|v| = √(9 + 16)
|v| = √25
|v| = 5
Try it yourself
Find the magnitude of v = (6, 8).
Show solution
Kiçik test
Biliklərini yoxla
Sual sırası hər dəfə dəyişir. Nəticəni testin sonunda görəcəksən.
Hazırsansa, 5 qısa sualdan ibarət testi başlat. Daxil olmadan da sınaqdan keçirə bilərsən.
Summary
- • Vectors have magnitude and direction.
- • A 2D vector can be written as (x, y).
- • Magnitude is found using the Pythagorean theorem.
Next lesson
Vector Addition →
Demo only — coming soon.