Introduction To Three Dimensional Geometry
* The coordinate space together with the coordinate axis is called the coordinate system.
* The coordinate axes divide the coordinate space into parts, called octants.
* Any point that lies on the X-axis will have its coordinates in the form (x, 0, 0).
* Any point that lies on the Y-axis will have its coordinates in the form (0, y, 0).
* Any point that lies on the Z-axis will have its coordinates in the form (0, 0, z).
* Any point on the XY plane will be of the form (x, y, 0).
* Any point on the YZ plane will be of the form (0, y, z).
* Any point on the ZX plane will be of the form (x, 0, z).
Distance Between Two Points
Distance between two points having coordinates ( x_{1}, y_{1} , z_{1} ) and ( x_{2}, y_{2} , z_{2} )
= \sqrt{( x_{2} - x_{1} )² + ( y_{2} - y_{1} )² + ( z_{2} - z_{1})² }
Distance of a point (x, y, z) from origin = \sqrt{( x² + y² + z² }
Section Formula
The coordinates of the points that the divides the line segment joining the points
( x_{1}, y_{1} , z_{1} ) and ( x_{2}, y_{2} , z_{2} ) in the ratio m:n are
C = ( \frac{m x_{2} + nx_{1} }{m +n} , \frac{m y_{2} + ny_{1} }{m +n} , \frac{m z_{2} + nz_{1} }{m +n} )
The coordinates of the points that divide the line segment joining the points
( x_{1}, y_{1} , z_{1} ) and ( x_{2}, y_{2} , z_{2} ) in the ratio 1:k are
C = ( \frac{x_{1} + kx_{2} }{1 + k} , \frac{y_{1} + ky_{2} }{1 + k} , \frac{z_{1} + kz_{2} }{1 +k} )