Find the coordinates of the point which divides that line segment joining the points
(-2, -2, -2) and (1, 4, 6) in the ratio (i) 2 : 3 internally, (ii) 2 : 3 externally.

Explanation

Let `P(-2,3,5) ` and `Q(1,-4,6)` are the given points and we have to find coordinates of point `R(x,y,z)`.

(i) Coordinates of a point which divides the line internally in ratio `m:n` are given by

`((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n),(mz_2+nz_1)/(m+n))`

Here, `m:n` = `2:3`.

So, `R(x,y,z) = ((2(1)+3(-2))/(2+3),(2(-4)+3(3))/(2+3),(2(6)+3(5))/(2+3))`

`= (-4/5,1/5,27/5)`




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