Perpendicular Symbol in LaTeX

Write perpendicular as \perp: AB \perp CD. Parallel is \parallel, and the negations are \not\perp and \nparallel (amssymb). For an orthogonal complement put \perp in a superscript: W^{\perp}.

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Perpendicular and parallel

a \perp b
$a ⊥ b$
⊥ as a relation, with space on both sides.
a \not\perp b
$a ⊥̸ b$
Not perpendicular.
a \parallel b
$a ∥ b$
∥ parallel.
a \nparallel b
$a ∦ b$
∦ not parallel (amssymb).
W^{\perp}
$W^{⊥}$
Orthogonal complement.
\bot
$⊥$
⊥ as an ordinary symbol (logic "false", bottom element).

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Perpendicular and parallel examples

Each result below is drawn from the LaTeX under it. Copy the code, edit it on this page, or open it in the full editor.

Perpendicular lines
$\overset{―}{A B} ⊥ \overset{―}{C D}$
LaTeX
```
\overline{AB} \perp \overline{CD}
```
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Orthogonal vectors
$u ⊥ v ⟺ u \cdot v = 0$
LaTeX
```
u \perp v \iff u \cdot v = 0
```
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Parallel lines
$ℓ_{1} ∥ ℓ_{2}$
LaTeX
```
\ell_1 \parallel \ell_2
```
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Orthogonal complement
$V = W \oplus W^{⊥}$
LaTeX
```
V = W \oplus W^{\perp}
```
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Not parallel
$ℓ_{1} ∦ ℓ_{3}$
LaTeX
```
\ell_1 \nparallel \ell_3
```
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Independence in probability
$X ⊥ Y ∣ Z$
LaTeX
```
X \perp Y \mid Z
```
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\perp or \bot

Both draw ⊥. \perp is a relation (space on both sides), right between two objects. \bot is an ordinary symbol, used for "false" in logic and the bottom element of a lattice. In superscripts the difference disappears, so W^{\perp} and W^{\bot} look the same.

Parallel and the norm bars

\parallel is a relation like \perp. The same double bar written as \| is an ordinary symbol used for norms, so do not use \| for "is parallel to".

Common mistakes

\bot has no relation spacing, so the letters crowd the symbol.
Instead of
```
a \bot b
```
Write
```
a \perp b
```
Two keyboard bars are two separate symbols with a gap.
Instead of
```
l_1 || l_2
```
Write
```
\ell_1 \parallel \ell_2
```
\nparallel comes from amssymb.
Instead of
```
a \nparallel b  (no amssymb)
```
Write
```
\usepackage{amssymb}
```

In Overleaf, MathJax and Word

Overleaf and pdfLaTeX
\perp, \parallel, \bot need nothing; \nparallel needs amssymb.
MathJax and KaTeX
MathJax and KaTeX support all commands on this page.
Microsoft Word
In a Word equation \perp then Space gives ⊥ and \parallel gives ∥.

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Perpendicular and parallel in LaTeX: questions

What is the LaTeX command for perpendicular?: \perp.
How do I write the orthogonal complement?: W^{\perp}.
How do I write parallel lines?: \ell_1 \parallel \ell_2.

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Perpendicular Symbol in LaTeX

Perpendicular and parallel

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Perpendicular and parallel examples

Perpendicular lines

Orthogonal vectors

Parallel lines

Orthogonal complement

Not parallel

Independence in probability