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Question -

Find the ratio in which the line joining (2, 4, 5) and (3, 5, 4) is divided by the yz-plane.



Answer -

Given:
The points (2, 4, 5) and (3, 5, 4)
By using the section formula,
 
We know X coordinate is always 0 on yz-plane
So, let Point C(0, y, z), and let C divide AB in ratio k: 1
Then, m = k and n = 1
A(2, 4, 5) and B(3, 5, 4)
The coordinates of C are:
On comparing we get,
[3k + 2] / [k + 1] = 0
3k + 2 = 0(k + 1)
3k + 2 = 0
3k = – 2
k = -2/3
∴We can say that, C divides AB externally in ratio 2: 3

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