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