VEC004 · Vectors · Classes 11–12
Unit vector
A unit vector has length 1. Dividing a vector by its magnitude gives the unit vector in its direction.
v̂Unit vector
📐 Formula
v̂ = v / |v|
✏️ Worked example
v = (3, 4), |v| = 5, so v̂ = (0.6, 0.8).
🌍 Where it is used
Directions in graphics and physics without size.
❓ Quick check
Unit vector along (0, −7)?
🏋️ Practice
EasyUnit vector along 5i?
Answer: i
MediumUnit vector along (1, 1)?
Answer: (1/√2, 1/√2)
ChallengeA vector of length 10 along (3, 4)?
Answer: (6, 8)