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 - Maths - Introduction to Three Dimensional Geometry

Question

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

Ajanta Trivedi · Accepted Answer

let the given points are A(2, -1, 3) and B(-1, 2, 1).

let the line segment AB is divided by the plane x+y+z = 5.......(1) in the ratio k : 1.

therefore by the section formula: coordinates of the intersecting point are

$(\frac{2 - k}{k + 1}, \frac{- 1 + 2 k}{k + 1}, \frac{3 + k}{k + 1})$

this point must lie on the given plane (1):

$\frac{2 - k}{k + 1} + \frac{- 1 + 2 k}{k + 1} + \frac{3 + k}{k + 1} = 5 \frac{4 + 2 k}{k + 1} = 5 4 + 2 k = 5 k + 5 3 k = - 1 \Rightarrow k = - \frac{1}{3}$

thus it divides externally in the ratio 1 : 3.

hope this helps you.

cheers!!