1. 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

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

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

thus it divides externally in the ratio 1 : 3.

hope this helps you.

cheers!!

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