Question

please only find the ratio and show me how. step by step. #3D geometry

Answer 1

for collinearity prove that the area of traingle formed by the three points is zero.

or other way is to write the equation of the line by taking any two points.
and then put the value of third point in the equation , if the equation satsifies then they line on the same line else doesn't.

let point divide the line in ratio m:n

then we know that the formula
(mx2+ nx1)/(m+n) ,(my2 +ny1)/m+n,(mz2 +nz1)/m+n,

is the point that divides the line in that ratio.

so 5 = 3n+9m/(m+n)
5m+5n=3n+9m
2n=4m
m/n = 1/2

therefore ratio is 1:2