The $x$-axis and the line through $(0, 0, 1)$ parallel to the $y$-axis in $\reals^3$

Example · High school

Terms

Term	This example	Why
orthogonal	✓	The $x$-axis and the line through $(0, 0, 1)$ parallel to the $y$-axis have orthogonal direction vectors $(1, 0, 0)$ and $(0, 1, 0)$, so the lines are orthogonal.
perpendicular	✗	The $x$-axis and the line through $(0, 0, 1)$ parallel to the $y$-axis are not perpendicular, because the lines never intersect: the first line has $z = 0$ and the second line has $z = 1$.
right angle	✗	The $x$-axis and the line through $(0, 0, 1)$ parallel to the $y$-axis do not form a right angle, because the lines have no common point at which to form an angle.

Distinctions using this example

• Right angle vs. perpendicular vs. orthogonal vs. normal: The $x$-axis and the line through $(0, 0, 1)$ parallel to the $y$-axis show that orthogonal lines need not intersect, so orthogonal lines need not be perpendicular.

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