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Question

The angle between the straight lines, whose direction cosines are given by the equations 2l+2mn=0 and mn+nl+lm=0, is

A
π3
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B
π2
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C
πcos1(49)
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D
cos1(89)
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Solution

The correct option is B π2
2l+2mn=0(i)
and mn+nl+lm=0(ii)
From equation (i) and (ii)
(m+l)(2l+2m)+lm=0
2l2+5lm+2m2=0
2l2+4lm+lm+2m2=0
2l(l+2m)+m(l+2m)=0
(2l+m)(l+2m)=0
Direction ratios of lines are (1,2,2) and (2,1,2).
Here l1l2+m1m2+n1n2=0
Lines are perpendicular to each other.

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