# Section / ratio – 3 dimensions Calculator

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.

Formula

Ratio Externally
(mx2-nx1/m-n , my2-ny1/m-n , mz2-nz1/m-n)

Ratio Internally
(mx2+nx1/m+n, my2+ny1/m+n  , mz2+nz1/m+n

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 = 2, y2 = 1, z2 = 3
m = 1, n = 2

Apply Formula:
(mx2+nx1/m+n , my2+ny1/m+n , mz2+nz1/m+n)
(1*2+2*1/1+2, 1*1+2*2/1+2 , 1*3+2*3/1+2)
(2+2/3, 1+4/3, 3+6/3)
(4/3, 5/3, 9/3)
(1.3, 1.6, 3)

Case 2: Find the coordinates of the point which divides the line joining the points (1, 3, 5), (2, 3, 4) externally in the ratio 2:3.
x1 = 1, y1 = 3, z1 = 5 and
x2 = 2, y2 = 3, z2 = 4
m = 2, n = 3

Apply Formula
(mx2-nx1/m-n , my2-ny1/m-n , mz2-nz1/m-n)
(2*2-3*1/2-3 , 2*3-3*3/2-3 , 2*4-3*5/2-3)
(4-3/-1 , 6-9/-1 , 8-15/-1)
(1/-1 , -3/-1 , -7/-1)
(-1 , 3 , 7)