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,
x1 = -2, y1 = 4, z1 = 7;
x2 = 3, y2 = -5, z2 = 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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