A unit vector has length 1 — it carries direction without magnitude.
Drag the two vectors
|a| = √3²+0²
3
3
|b|
2
2
angle between ≈ 90° (perpendicular!)
a + b = (3, 2)
Normalising a vector
Divide a vector by its own magnitude and you get a unit vector — same direction, length exactly 1. Drag the vectors above and watch the magnitude readout.
Your turn
Find the unit vector in the direction of v = (3, 4).
Unit vectors are pure direction. To build any vector pointing 'that way' with length L, just multiply: v = L · û.
Normalize
Standard basis
- î = (1, 0, 0)
- ĵ = (0, 1, 0)
- k̂ = (0, 0, 1)