Hesse normal form
Hesse normal form is a way to describe a flat shape called a plane in a very useful way. Imagine a flat sheet of paper - that's a plane. Now imagine if you wanted to describe exactly where that sheet of paper was in space, you could do that using Hesse normal form.
Hesse normal form uses three numbers to describe the position of the plane. The first number tells you how far away the plane is from the origin point (which is kind of like the middle of everything). The second and third numbers tell you the direction that the plane is facing.
So imagine you're looking at that sheet of paper head-on. The first number in the Hesse normal form tells you how far away the paper is from you. The second and third numbers tell you which way the paper is facing - if the second number is positive, the plane is facing to your right, and if it's negative, it's facing to your left. The third number tells you if the plane is facing up (positive) or down (negative).
Now imagine if you wanted to describe a different plane - maybe one that's not facing straight ahead. You could use Hesse normal form to do that too. You just need to figure out the distance from the origin point like before, and then the two directions that the plane is facing - one horizontal and one vertical. These directions are called "normal vectors" and they tell you how the plane is tilted.
So Hesse normal form is just a way to describe a plane using three numbers - one that tells you how far away it is, and two vectors that tell you how it's facing. It makes it easy to work with planes and figure out things like how they intersect with other shapes.
Hesse normal form uses three numbers to describe the position of the plane. The first number tells you how far away the plane is from the origin point (which is kind of like the middle of everything). The second and third numbers tell you the direction that the plane is facing.
So imagine you're looking at that sheet of paper head-on. The first number in the Hesse normal form tells you how far away the paper is from you. The second and third numbers tell you which way the paper is facing - if the second number is positive, the plane is facing to your right, and if it's negative, it's facing to your left. The third number tells you if the plane is facing up (positive) or down (negative).
Now imagine if you wanted to describe a different plane - maybe one that's not facing straight ahead. You could use Hesse normal form to do that too. You just need to figure out the distance from the origin point like before, and then the two directions that the plane is facing - one horizontal and one vertical. These directions are called "normal vectors" and they tell you how the plane is tilted.
So Hesse normal form is just a way to describe a plane using three numbers - one that tells you how far away it is, and two vectors that tell you how it's facing. It makes it easy to work with planes and figure out things like how they intersect with other shapes.