Two orthogonal vectors

The two vectors in $\mathbb{R}^3$ :

(1) $\begin{align*} x &= \begin{pmatrix} 1 \\ 1 \\ 3 \end{pmatrix} \end{align*},$

(2) $\begin{align*} y &= \begin{pmatrix} 4 \\ -1 \\ -1 \end{pmatrix} \end{align*}$

are orthogonal, since

$x^T y=\underbrace{1 \times 4}_{x_1 \times y_1}+\underbrace{1 \times(-1)}_{x_2 \times y_2}+\underbrace{(-1) \times 3}_{x_3 \times y_3}=0 .$

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