Orthogonal vectors

Definition

Let $V$ be an inner product space over $\R$ or $\C$. Two vectors $x, y \in V$ are orthogonal, written $x \perp y$, when $\langle x, y \rangle = 0$, where $\langle \cdot, \cdot \rangle$ is the inner product.

Remarks

The relation is symmetric, because $\langle y, x \rangle = \overline{\langle x, y \rangle}$. The zero vector is orthogonal to every vector, and it is the only vector orthogonal to itself. In $\R^2$ with the dot product, $(1, 2)$ and $(-2, 1)$ are orthogonal.

Explanations

L1 human

Orthogonal is the general word for perpendicular. Two vectors are orthogonal when their inner product is zero. In the plane and in space, this means that they meet at a right angle.