bot
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
l_1 \bot l_2
Denoting orthogonal vectors in linear algebra
\vec{u} \bot \vec{v} \implies \vec{u} \cdot \vec{v} = 0
Representing the orthogonal complement of a subspace
V^{\bot} = \{w \in W : w \bot v \text{ for all } v \in V\}