Given: points A(2, 4, 5) and B(3, 5, -9)
To find: the ratio in which the line joining given points is divided by the yz-plane
Formula used:
Section Formula:
A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).
The coordinates of C is given by,
\(\Big(\frac{nx+ma}{m+n},\frac{ny+mb}{m+n},\frac{nz+mc}{m+n}\Big)\)
x coordinate is always 0 on yz-plane
Let Point C(0, y, z) and C divides AB in ratio k : 1
Therefore, m = k and n = 1
A(2, 4, 5) and B(3, 5, -9)
Coordinates of C using section formula:
On comparing:
\(\frac{3k+2}{k+1}\) = 0
⇒ 3k + 2 = 0(k + 1)
⇒ 3k + 2 = 0
⇒ 3k = –2
⇒ k = \(\frac{-2}{3}\)
Hence, C divides AB externally in ratio 2 : 3
