Q. 34.4( 45 Votes )

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

Answer :

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).

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

Then,

Comparing this information with the details given in the question, 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 section formula,

We know that the coordinates of the point R which divides the line segment joining two points P (x_{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}) internally in the ratio m : n is given by:

So, we have

⇒ 3k – 2 = 0 ⇒ 3k = 2

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

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