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the straight lines whose direction cosines given by al+bm+cn=0 and mn+nl+lm=0 are parallel if a^1/2+b^1/2-c^1/2 is equal to a) 0,b) 1,c)2,d)4
Dear Vaibhav
al+bm+cn=0....................1
mn+nl+lm=0......................2
put value of n from 1 to second and form the quadretic equation in (l/m)
a(l/m)2 +(a+b-c)(l/m) +b=0
so (l1/m1)*(l2/m2) =b/a ...............3
given line are parallel so l1/l2 =m1/m2 =n1/n2
or l1/m1 =l2/m2
so from equation 3
l1/m1 =(b/a)1/2
and l1/m1 +l2/m2 =(c-a-b)/a
or 2(l1/m1) =(c-a-b)/a
from above result
2(b/a)1/2=(c-a-b)/a
or a+b+ 2(ba)1/2=c
(a)1/2+ (b)1/2=(c)1/2
so option a is correct
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