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Q.

A,B,C and D are any four points in the space. If AB×CD+BC×AD+CA×BD=λABC , where ABC is the area of traingle ABC, then λ is equal to

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a

2

b

1/2

c

4

d

1/4

answer is C.

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Detailed Solution

    OA=o    OB=b   OC=c   OD =d     b×(d-c)+(c-b)×d+(-c)×(d-b) =b×d-b×c+c×d-b×d-c×d+c×b =2b×c=4.12b×c                   =4 area ABC

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