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Represents perpendicularity in mathematics and geometry, indicating when two lines or vectors meet at right angles.

Overview

Essential in geometric proofs, linear algebra, and vector analysis where perpendicular relationships need to be expressed clearly and formally.

  • Commonly used in coordinate geometry to denote orthogonal vectors or lines
  • Appears frequently in physics and engineering when describing forces or components at right angles
  • Used in mathematical logic as the "bottom" symbol to represent false or an undefined value
  • Helpful in architectural and technical drawings to indicate perpendicular construction elements

Examples

Expressing perpendicular lines in geometry

l1⊥l2l_1 \bot l_2 
l_1 \bot l_2

Denoting orthogonal vectors in linear algebra

u⃗⊥v⃗  ⟹  u⃗⋅v⃗=0\vec{u} \bot \vec{v} \implies \vec{u} \cdot \vec{v} = 0 
\vec{u} \bot \vec{v} \implies \vec{u} \cdot \vec{v} = 0

Representing the orthogonal complement of a subspace

V⊥={w∈W:w⊥v for all v∈V}V^{\bot} = \{w \in W : w \bot v \text{ for all } v \in V\} 
V^{\bot} = \{w \in W : w \bot v \text{ for all } v \in V\}