Plane that Passes Through the Origin
When (the origin), then the plane takes the vectorial representation:
We call this the plane that passes through the origin and is generated by the vectors and .
Does a Point Exist in a Plane?
To see if is in a given plane , then we can try to solve the equation system:
(remember we can write )
If the system can be solved, then the point exists in the plane. If it can’t be solved, then it doesn’t exist in the plane.
Plane that Passes Through 3 Points
Given 3 points , , , we can find the plane that passes through these three points by doing the following:
- Choosing one point as the base point. Let’s say we choose
- Calculating the direction vectors by subtracting the base point from the other points:
- We can use the base point and these two vectors to represent the plane that passes through these three points