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Question

The acute angle between the lines whose direction ratios are given by l+mn=0 and l2+m2n2=0, is

A
0
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B
π/6
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C
π/4
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D
π/3
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Solution

The correct option is D π/3
We have
l+mn=0
and l2+m2+n2=0
l2+m2=n2 and l+m=n
l2+m2=(l+m)2
2lm=0
l=0,m=0
If l=0, then m=n
l0=m1=n1
If m=0, then
l=n
l1=m0=n1
thus, the dr's of the lines are proportional to 0,1,1 and 1,0,1
Therefore, angle θ between them is given by
cosθ=0×1+1×0+|1×1|0+1+11+0+1=12
θ=π3

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