TeXipedia

perp

Denotes perpendicularity between geometric objects, particularly lines, planes, or vectors in mathematics.

Overview

Essential in geometry, linear algebra, and vector analysis for expressing spatial relationships between mathematical objects.

  • Commonly used in geometric proofs to indicate lines or planes meeting at right angles
  • Appears frequently in vector space theory to denote orthogonal vectors
  • Important in physics and engineering when describing perpendicular forces or structural components
  • Used in coordinate geometry to specify perpendicular lines with slopes that are negative reciprocals

Examples

Denoting perpendicular lines in geometry

Line l1⊥l2\text{Line } l_1 \perp l_2 
\text{Line } l_1 \perp l_2

Expressing orthogonal vectors in linear algebra

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

Indicating independent events in probability theory

P(A⊥B)=P(A)⋅P(B)P(A \perp B) = P(A) \cdot P(B) 
P(A \perp B) = P(A) \cdot P(B)