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$If a △ A B C the mid points of the sides A B, B C, C A are respectively (l, 0, 0), (0, m, 0) and (0, 0, n)$ $then$
$\frac{A B^{2} + B C^{2} + C A^{2}}{l^{2} + m^{2} + n^{2}} =$

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Correct option is C

We have A+B=2l,0,0, B+C=0,2m,0 and C+A=0,0,2n ⇒A=l,-m,n, B=l,m,-n and C=-l,m,n ∴AB2+BC2+CA2l2+m2+n2=4m2+4n2+4l2+4n2+4l2+4m2l2+m2+n2=8

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If a △ABC the mid points of the sides AB,BC,CA are respectively (l,0,0),(0,m,0) and (0,0,n) thenAB2+BC2+CA2l2+m2+n2=

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Ready to Test Your Skills?

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$If a △ A B C the mid points of the sides A B, B C, C A are respectively (l, 0, 0), (0, m, 0) and (0, 0, n)$ $then$
$\frac{A B^{2} + B C^{2} + C A^{2}}{l^{2} + m^{2} + n^{2}} =$