Let the line segment joining the points A(–2, 4, 7) and B(3, –5, 8) be divided by the yz-plane at a point C in the ratio k : 1.
∴ Coordinates of C are
(

3k−2

k+1

,

−5k+4

k+1

,

8k+7

k+1

)
Since the point C lies on YZ-plane. So X = 0
∴

3k−2

k+1

= 0 ⇒ 3k - 2 = 0 ⇒ k =

2

3

Thus the required ratio is

2

3

: 1 i.e., 2 : 3