Vector arrow and hat (v⃗, x̂)

How to read it

OpenStax’s University Physics adopts the convention that a letter with an arrow above it is a vector and a letter without one is a scalar: a distance of 2.0 km is d, but a displacement of 2.0 km in some direction is d⃗. It writes î and ĵ for the positive x and y directions, and a vector as its parts along the axes, as in v⃗ = (4.0 î + 3.0 ĵ + 0.1 k̂) km/h. A unit vector of direction, such as v̂, is the vector divided by its own magnitude, and OpenStax points out that it has no unit. Both marks appear together in Newton’s law of gravitation as OpenStax writes it, F⃗₁₂ = G m₁m₂/r² r̂₁₂, where r̂₁₂ is the unit vector pointing from one object to the other.

Also searched as: arrow over a letter, hat symbol, i hat, j hat, k hat, unit vector symbol, vector arrow, vector arrow and hat symbol, v⃗, x̂, x hat.

Bold instead of an arrow

Printed books often use bold type in place of the arrow. NIST’s Guide for the Use of the SI says symbols for vectors are bold italic, and the IUPAC Green Book says vectors shall be printed in bold italic, as F for force and r for position, with plain italic r for the size of the vector, |r|. The Green Book allows the arrow as the alternative, and writes the unit vectors along the axes as eₓ, e_y, e_z or as bold i, j, k, with no hats.

Other hats

Outside vector work a hat means something else. In quantum mechanics it marks an operator: the Green Book writes the momentum operator p̂ and the hamiltonian Ĥ. In statistics it marks an estimate, as in ŷ, and a bar over a letter is a mean, as in x̄. A dot over a letter is a time derivative (ẋ).

Typing them

Unicode has a combining right arrow above (U+20D7), which its chart marks as the vector arrow; typed after a letter it sits over it.