Answer :

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


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