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
(

9k+3

k+1

,

8k+2

k+1

,

−10k−4

k+1

)
But it is given that coordinates of Q are (5, 4, –6)
∴

9k+3

k+1

= 5 ⇒ 9k + 3 = 5k + 5 ⇒ 4k = 2 ⇒ k =

1

2

Thus Q divides the line segment joining the points P and R in the ratio

1

2

: 1 i.e., 1 : 2