## Problem on finding a normal vector of a 2d line

Find a normal vector to the 2d line $2x - y = 5$.
• ## Solution

Recall the relationship between a line in 2d and its normal vector:
To find $\bfn$, we should write the given line in this form.
Let $\bfn = (n_1, n_2)$ and $\bfx = (x, y)$.
Recall that
The line $\bfn \cdot \bfx = b$ is the same as $n_1 x + n_2 y = b$.
We identify that $n_1 = 2$, $n_2=-1$, and $b = 5$.
That is, the line can be written in the form $$(2, -1)\cdot(x,y) = 5.$$
We conclude that a normal vector to the line $2x-y=5$ is $\bfn = (2, -1)$.