Revision sheet · Mathematics

Three-dimensional geometry

Distance between two points in space: $d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2}$
Section formula in space: $P = (\frac{m _{1} x _{2} + m _{2} x _{1}}{m _{1} + m _{2}}, \frac{m _{1} y _{2} + m _{2} y _{1}}{m _{1} + m _{2}}, \frac{m _{1} z _{2} + m _{2} z _{1}}{m _{1} + m _{2}})$
Centroid of a triangle in space: $G = (\frac{x _{1} + x _{2} + x _{3}}{3}, \frac{y _{1} + y _{2} + y _{3}}{3}, \frac{z _{1} + z _{2} + z _{3}}{3})$