Question

Find the coordinates of the point which divides the join of the points P(5, 4, 2) and Q(-1, -2, 4) in the ratio 2:3.

Answer 1

Let R(x, y, z) be the required point. Then,

$x=\frac{2(-1)+3\times 5}{2+3},y=\frac{2(-2)+3\times 4}{2+3},z=\frac{2\times 4+3\times 2}{2+3}$

or $x=\frac{13}{5},y=\frac{8}{5}$ and $z=\frac{14}{5}$.

So, the required point is $R(\frac{13}{5},\frac{8}{5},\frac{14}{5})$.