Let Q(5, 4, –6) divides the line segment joining the points P(3, 2, –4) and R(9, 8, –10) in the ratio k : 1 internally. ∴ Then coordinates of Q are $\left( \frac{9k+3}{k+1} , \frac{8k+2}{k+1} , \frac{-10k-4}{k+1} \right)$ But it is given that coordinates of Q are (5, 4, –6) ∴ $\frac{9k+3}{k+1}$ = 5 ⇒ 9k + 3 = 5k + 5 ⇒ 4k = 2 ⇒ k = $\frac{1}{2}$ Thus Q divides the line segment joining the points P and R in the ratio $\frac{1}{2}$ : 1 i.e., 1 : 2