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Question

If the points A(3, 2, -4), B (9, 8, -10) and C(5, 4, -6) are collinear, find the ratio in which C divides AB.


Solution

Suppose C divides AB in the ratio \(\lambda : 1)

Then, coordinates of C are as follows :

(9λ+3λ+1,8λ+2λ+1,10λ4λ+1)

But, the coordinates of C are (5, 4, -6)

9λ+3λ+1=5,8λ+2λ+1=4,10λ4λ+1=6

These three equations give λ=12

So, C divides AB in the ratio 1 : 2.


Mathematics
RD Sharma
Standard XI

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