Given: points A(4, 8, 10) and B(6, 10, -8)
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,
\(\Big(\frac{nx+ma}{m+n},\frac{ny+mb}{m+n},\frac{nz+mc}{m+n}\Big)\)
the 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(4, 8, 10) and B(6, 10, -8)
Coordinates of C using section formula:
On comparing:
\(\frac{6k+4}{k+1}\) = 0
⇒ 6k + 4 = 0(k + 1)
⇒ 6k + 4 = 0
⇒ 6k = – 4
⇒ k = \(\frac{-4}{6}\)
⇒ k = \(\frac{-2}{3}\)
Hence, C divides AB externally in ratio 2 : 3