The vector $(1, 1)$ and the line $x + y = 1$ in the plane, whose direction vector is $(1, -1)$

Terms

Term	This example	Why
normal vector	✓	The vector $(1, 1)$ is a normal vector to the line $x + y = 1$, because $(1, 1)$ is the gradient of $x + y$, and the gradient is perpendicular to each level set.
orthogonal	✓	The vector $(1, 1)$ is orthogonal to the direction vector $(1, -1)$ of the line $x + y = 1$, because their dot product is $1 - 1 = 0$.
perpendicular	✗	The vector $(1, 1)$ and the line $x + y = 1$ are not called perpendicular, because “perpendicular” describes two lines or planes that intersect; the normal line through $\left(\frac{1}{2}, \frac{1}{2}\right)$ in the direction $(1, 1)$ is perpendicular to the line $x + y = 1$.

Right angle vs. perpendicular vs. orthogonal vs. normal: The vector $(1, 1)$ and the line $x + y = 1$ show that a normal vector is described relative to a shape: the vector is normal to the line and orthogonal to its direction vector.