How to know if N is normal to the plane or not? I have N = &lt;1 , -2 , 3 > and the plane 2x - 4y + 6z = 5
How do i know if N is normal to the plane or not? please be detailed with the answer as i'm very lost.
Hint The normal of any plane $ax + by + cz = d$ is $(a,b,c)$, hence in this case $(2,-4,6)$.

Now, is your $N = (1, -2, 3)$ parallel to $(2, -4, 6)$?
In the equation for a plane the  coefficients of each of the coordinates tells you the direction that is perpendicular to the plane. You can tell if the vector given is perpendicular by measuring the angle between it and the perpendicular vector. How to do that is a matter of choice. I think easiest in this case is to note that 2*N is gives the coefficients so obviously N is parallel and thus perpendicular to the plane.