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 Internally:
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 :
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 :
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.
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