First slide

Direction ratios and direction cosines

Question

In a $Δ A B C$ the mid points of the sides AB,BC,CA are respectively (l,0,0), (0,m,0) and (0,0,n). Then $\frac{A B^{2} + B C^{2} + C A^{2}}{l^{2} + m^{2} + n^{2}} =$

Moderate

A

2
B

4
C

8
D

16

Solution

$A B^{2} = 4 (m^{2} + n^{2})$ , $B C^{2} = 4 (l^{2} + n^{2})$
$A C^{2} = 4 (l^{2} + m^{2})$

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