Find the ratio in which the line segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z = 5.
Given: A(2, -1, 3) and B(-1, 2, 1)
To find: the ratio in which the line segment AB is divided by the plane x + y + z = 5
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,
Let C(x, y, z) be any point on the given plane and C divides AB in ratio k: 1
Therefore, m = k and n = 1
A(2, -1, 3) and B(-1, 2, 1)
Coordinates of C using section formula:
On comparing:
Since, x + y + z = 5
⇒ 5(k + 1) = 4
⇒ 5k + 5 = 4
⇒ 5k = 4 – 5
⇒ 5k = – 1
Hence, the plane divides AB externally in ratio 1:5