this is my first question here.
Suppose I have a surface as follow:
The gradient of the surface at a particular point $P = (x_0,y_0,z_0)$ is just $(2x_0,2y_0,2z_0)$ and the parametric equation of the line is $x(t) = x_0 + t(2x_0)$ and so on. Now how can we find the points that have their normal passing through the origin?
Normally I would set $P = (0,0,0)$ and the direction vector would remain. But here the direction vector is directly dependent on the point chosen, so if I were to set $P = (0,0,0)$, then there would be no line as well.
Could you guys help me with this?