# Cutting plane

Section plane of two spheres

The term cutting plane has several meanings in mathematics .

## The cutting plane as a result

In geometry , the term refers to a plane that is defined as the intersection of several bodies in a three-dimensional vector space .

### Application examples

• To calculate the circle of intersection of two balls , the cutting plane in which the circle of intersection lies is determined in order to then intersect with the straight line connecting the ball centers in order to determine the center of the circle of intersection.
• Alternatively, this formula can also be used to determine the center point of the intersection circle from the radii and the distance between the center points of the given spheres without having to set up a cutting plane or connecting line.

${\ displaystyle M_ {1}}$ = Center of the first sphere

${\ displaystyle M_ {2}}$ = Center of the second sphere

${\ displaystyle d}$= Distance between and${\ displaystyle M_ {1}}$${\ displaystyle M_ {2}}$

${\ displaystyle {\ vec {M}} _ {3} = {\ vec {M}} _ {1} + \ left ({\ frac {r_ {1} ^ {2} -r_ {2} ^ {2 }} {2d ^ {2}}} + 0 {,} 5 \ right) \ cdot ({\ vec {M}} _ {2} - {\ vec {M}} _ {1})}$

The center of the cutting circle is also a point on the cutting plane and the vector between the two centers also represents the normal vector of the cutting plane, so that the cutting plane can be set up from it.

## The cutting plane as a parameter

Also in geometry , the term can also denote a plane that is intersected with a body in order to consider the points of the body that lie on this cutting plane.