VG3
linear-algebra
Quiz
What are vectors?
A vector is a quantity with both magnitude and direction. Vectors are used everywhere — from physics and navigation to 3D graphics and machine learning.
What is a vector?
⃗v = (x, y)
Example: ⃗v = (3, 4) means 3 units in x-direction and 4 units in y-direction.
Magnitude
|⃗v| = √(x² + y²)
|(3, 4)| = √(9+16) = 5
Addition
⃗a + ⃗b = (a₁+b₁, a₂+b₂)
Dot product
⃗a · ⃗b = a₁·b₁ + a₂·b₂
If the dot product is 0, the vectors are perpendicular.
cos(θ) = (⃗a · ⃗b) / (|⃗a| · |⃗b|)
To those who do not know mathematics it is difficult to get across a real feeling as to the beauty of nature — the deep beauty of nature.
— Richard Feynman (1918–1988)
🧠 Test yourself
Question 1 of 3
What is the magnitude of the vector (3, 4)?