the.com/unit vector
All direction, no size — a vector that went on a diet to length one.
means A vector with magnitude exactly 1, used purely to indicate direction without contributing any scale or size.
from 'Vector' traces to Latin vehere, 'to carry' — a vector literally 'carries' a point from one place to another, a sense borrowed into math and physics in the 1800s via astronomy's 'radius vector.' 'Unit' comes from Latin unus, 'one.' The term 'unit vector' itself is a 19th/20th-century mathematical coinage, paired with the practice of 'normalizing' a vector — dividing it by its own length so only direction survives, leaving the number 1 as the quiet proof that all the bulk has been carried away.
- magnitude
- always exactly 1, no exceptions
- formula
- divide any vector by its own length
- notation
- wears a hat symbol, literally called hat
- purpose
- points the way, lets magnitude live elsewhere