Question

Find the coordinates of the point, which divides the line segment joining the points $(-2,3,5)$ and $(1,-4,6)$ internally and externally in the ratio $2:3$

Answer 1

Let $A=(-2,3,5)$ and $B=(1,-4,6)$.

Let $C$ divide $AB$ internally in the ratio $2:3$

Then:

$C=\frac{2B+3A}{2+3}=(\frac{-4}{5},\frac{1}{5},\frac{27}{5})$

Let $D$ divide $AB$ externally in the ratio $2:3$

Then:

$D=\frac{2B-3A}{2-3}=3A-2B=(-8,17,3)$