Dick said:A plane has the same normal everywhere, doesn't it?
mharten1 said:That's what I thought at first. But it seems too easy to be the solution to both questions. I'm going to read over the section again and see if I can find anything that will be useful.
Dick said:It's not the solution to the second question. Think about using the gradient.
A vector normal to a plane is a vector that is perpendicular to every vector in the plane. It is also known as the surface normal or simply the normal vector.
A vector normal to a plane can be calculated by finding the cross product of two non-parallel vectors in the plane. The resulting vector will be perpendicular to both of the original vectors and therefore normal to the plane.
It is important to find a vector normal to a plane because it can be used to calculate the angle between the plane and another vector, determine the direction of the plane, and solve various geometrical problems involving the plane.
No, a plane can only have one vector normal. This is because if two vectors are perpendicular to a plane, they must also be parallel to each other, which is not possible.
To find a vector normal to a plane at a specific point, you can use the formula:
n = (ax + by + cz) / sqrt(a^2 + b^2 + c^2), where a, b, and c are the coefficients of the plane's equation and (x, y, z) is the point of interest. This will give you a vector that is perpendicular to the plane at the given point.