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Question

The direction cosines of two lines satisfy the relations λ(l+m)=n and mn+nl+lm=0.The value of λ, for which the two lines are perpendicular to each other, is

A
1
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B
2
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C
12
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D
4
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Solution

The correct option is B 2
By Eliminating n, we get
λ(l+m)2+lm=0λl2m2+(2λ+1)lm+λ=0lll2m1m2=1
Where l1m1 and l2m2 are the roots of this equation, Further eliminating m, we get
λl2lnn2=0l1l2n1n2=1λ
Since, the lines with direction cosines (l1,m1,n1) and (l2,m2,n2) are perpendicular.
l1l2+m1m2+n1n2=0
1+1λ=0λ=2

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