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Question

Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, –8) is divided by the yz-plane.


Solution

Let A = (4, 8, 10) , B = (6, 10, -8)
Let the line joining A and B be divided by the YZ-plane at point P in the ratio λ:1.
P=6λ+4λ+1, 10λ+8λ+1, -8λ+10λ+1
Since P lies on the YZ-plane, the x-coordinate of P will be zero.
6λ+4λ+1=06λ+4=06λ=-4 λ=-23
Hence, the YZ-plane divides AB in the ratio 2:3 (externally)

Mathematics
RD Sharma XI (2015)
Standard XI

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