How to make the orthogonal symbol in LaTeX ?

How to make the perpendicular symbol in LaTeX ?

Here are some examples using the \perp command.

Orthogonality of two vectors: orthogonal symbol in Latex

Let $u$ and $v$ be two vectors, to express that $u$ and $v$ are orthogonal, we can write :

u \perp v
\[\begin{equation} u \perp v \end{equation}\]

Orthogonality of a line and a vector: orthogonal symbol in Latex

Let $w$ be a vector and $d$ a line, to express that $w$ is orthogonal to $d$, we can write :

w \perp \bar{d}
\[\begin{equation} w \perp \bar{d} \end{equation}\]

Orthogonality in the Hilbert sense: orthogonal symbol in Latex

In addition to the previous cases, it is also possible to express orthogonality in the Hilbert sense. Given two vectors $x$ and $y$, to express that $x$ and $y$ are orthogonal in the Hilbert sense, we can write the scalar product :

\langle x, y \rangle = 0
\[\begin{equation} \langle x, y \rangle = 0 \end{equation}\]

where $\langle \cdot, \cdot \rangle$ represents the scalar product of two vectors.