If we have a vertical line $x=c$ or a horizontal line $y=c$ what are the normal vectors for these?
For example, I know that the normal vector for $y=c-x$ is $<1,1>$ so I imagine that for the horizontal and vertical cases it is $<0,1>$ and $<1,0>$? But I am not sure which one is which or if that is even correct.
Is there a way to explicitly calculate this?
Thanks.
You are right, the normal vector to $y = c$ is $(0,1)$ and the normal vector to $x = c$ is $(1,0)$ (where by normal I mean on of the two orthonormal vector of norm $1$). In general for a line of equation $ax+by+c=0$ the normal vector is $$ \left( \frac{a}{\sqrt{a^2+b^2}}, \frac{b}{\sqrt{a^2+b^2}} \right) $$ Indeed, since the family parametrized by $c$ is made of parallel lines it is enough to find the normal vector to the line $ax + by = 0$. Now, being tangent means to have scalar product zero with any point in the line. From the equation you see that $(a,b)$ is a vector that has this property. Therefore, you only need to normalize it.