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Q.

In a  ΔABC the mid points of the sides AB,BC,CA are respectively (l,0,0), (0,m,0)  and (0,0,n). Then AB2+BC2+CA2l2+m2+n2=

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a

2

b

4

c

8

d

16

answer is C.

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Detailed Solution

AB2=4(m2+n2), BC2=4(l2+n2)AC2=4(l2+m2)
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In a  ΔABC the mid points of the sides AB,BC,CA are respectively (l,0,0), (0,m,0)  and (0,0,n). Then AB2+BC2+CA2l2+m2+n2=