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# If the direct cosines of two lines are such that l+m+n=0, l2+m2-n2=0, then the angle between them is ?

Vikas TU
14149 Points
4 years ago
Dear Student,
l+m+n=0 => l+m=−n => −(l+m) = n -------- (1)
and l2+m2−n2=0 ----- (2)
Substitute for n in equation (2) we get l2+m2−l2−m2−2ml=0 or 2ml=0 =>  l=0 or m=0.
Put m=0 in equation (1). If m=0, then l=−n and direction ratios are (l,m,n)=(1,0,−1).
Let us put l=0, we get m=−n, direction ratios are (l,m,n)=(0,1,−1).
(l1, m1, n1).(l2, m2, n2) = (1,0,−1).(0,1,−1) = 0+0+1 = 1
Now substituting the above values in
cosθ = b1.b2/|b1||b2|
cosθ = 1/√2√2 = 1/2 => θ= π/3.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)