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Question

The direction cosines l,m,n of two lines are connected by the relations l+m+n=0, lm=0, then the angle between them is

A
π3
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B
π4
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C
π2
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D
0
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Solution

The correct option is A π3
Given, l+m+n=0.....(i)

And lm=0

Either, m=0 or l=0

If l=0, then put in eq (i) we get m=n

Direction ratios are 0.n,n i.e., 0,1,1

If m=0, then put in eq.(i) we get l=n

Direction ratios are n,0,n i.e.,1,0,1

cosθ=0(1)+(1)×0+1×1(0)2+(1)2+(1)2(1)2+(0)2+(1)2=12

θ=π3

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