Q.
Find the angle between the lines whose direction cosines satisfy the equations
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Detailed Solution
i) Given equations are l + m + n = 0 ..... (1)
From eq (1), l = – m – n
Substituting in equation (2)
Case (i): put m = 0 in eq (1)
dr’s of first line are (– 1, 0, 1)
dc’s of first line are (l1, m1, n1) =
Case (ii): put m = –n in (1)
dr’s of second line are= (a, b, c) = (0, –1, 1)
dc’s of second line are (l2, m2, n2) =
Let be angle between the lines then
ii) Given equations are
3l + m + 5n = 0 ..... (1)
6mn - 2nl + 5lm = 0 ...... (2)
From eq (1), m = –3l – 5n
Substituting in equation (2)
Case (i):
From eq (1),
dr’s of first line are= (a, b, c) = (–1, –2, 1)
dc’s of second line are =
Case (ii): If
From eq (i),
dr’s = (a, b, c) = (–2, 1, 1)
dc’s = (l2, m2, n2) =

