Let the line segment formed by joining the points P (-2, 4, 7) and Q (3, -5, 8) be PQ.

We know that any point on the YZ-plane is of the form (0, y, z).

So now, let R (0, y, z) divides the line segment PQ in the ratio k: 1.

Then, comparing we have,

x_{1} = -2, y_{1} = 4, z_{1} = 7;

x_{2} = 3, y_{2} = -5, z_{2} = 8 and

m = k, n = 1

By using the section formula,

\((0,y,z)= \dfrac{k(3)-2}{k+1}, \dfrac{k(-5)+4}{k+1}, \dfrac{k(8)+7}{k+1} \)

The x coordinate is 0 on YZ-plane,

\( \dfrac{3k-2}{k+1}=0\)

3k – 2 = 0

3k = 2

k = \( \dfrac{2}{3}\)

Therefore, the ratio in which the YZ-plane divides the line segment joining the points (-2,4,7) and (3,-5,8) is 2:3.

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