Find the angle between the two lines whose direction cosines are given by the equations:
l + m + n = 0, l2 + m2 – n2 = 0
The given equation are
l + m + n = 0 ...(1)
and l2 + m2 – n2 = 0 ....(2)
From (1), n = – (l + m) ....(3)
From (2) and (3), we get,
l2 + m2 – (l + m)2 = 0 or – 2 l m = 0
⇒ l m = 0
either l = 0
1. l + 0 .m + 0. n = 0
Also, l+m+n = 0
Solving,
or m = 0
0.l + l.m + 0.n = 0
Also, l + m + n = 0
Solving,
∴ direction ratios of the two lines are 0, – 1, 1 ; 1, 0, – 1
Let θ be the angle between the lines
∴ acute angle θ between the lines is given by
