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Section or Ratio(3 dimension) Tutorial

  


Section or Ratio Definition:
     Ratio formula or section formula is used to find the coordinates of a point P which divides the segment joining the points A and B internally or externally in the ratio m : n on three dimension.

Section or Ratio Formula:

Ratio Externally:
ratio
Ratio Internally:
ratio
where
              (x1, y1, z1)   (x2, y2, z2) be the end points of a line segment.
              m:n is ratio externally are internally.

Section or Ratio Example:
Case 1: Find the coordinates of the point which divides the line joining the points (1, 2, 3), (1, 2, 3) internally in the ratio 1:2.

 x1 = 1, y1 = 2,  z1 = 3 and
 x2 = 1, y2 = 2,  z2 = 3
 m = 1, n = 2

  Substitute in the formula as :
            ratio
            ratio
Case 2: Find the coordinates of the point which divides the line joining the points (1, 3, 5), (2, 4, 6) internally in the ratio 2:3.

 x1 = 1, y1 = 3, z1 = 5 and
 x2 = 2, y2 = 4, z2 = 6
 m = 2, n = 3

  Substitute in the formula as :
            ratio
            ratio
The above example will clearly illustrates how to calculate the Coordinates of Point Externally/Internally using Section or Ratio formula on the three dimension manually.



Related Calculator:
>> Section or Ratio(3 dimension) Calculator.
This tutorial will help you dynamically to find the Analytical Geometry problems.