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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.


Solution

(2, -1, 3) and (-1, 2, 1)

x+y+z=5

Assume plane divides line in ratio λ:1

so point P which is dividing line in λ:1 ratio is

P=(λ+2λ+1,2λ1λ+1,λ+3λ+1)

P lies on plane x+y+z=5

λ+2+2λ1+λ+3=5λ+5

3λ=1λ=1:3

So plane dividing line in 1 : 3 ratio externally


Mathematics
RD Sharma
Standard XI

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