Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

Asked by Pragya Singh | 11 months ago |  107

##### Solution :-

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.

Answered by Abhisek | 11 months ago

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