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Find the angle between two lines whose directions cosines are given by l+m+n=0 and l^2+m^2-n^2=0.[**WITHOUT USING THEOREMS OF VECTOR**]
Asked by arjunsah797 | 02 May, 2022, 09:30: AM
Given direction cosines are
l+m+n = 0 ... (i)
l2 + m2 - n2 = 0 ... (ii)
From (i), we get, n = -(l+m)
Putting n in (ii)
l2 + m2 - (l+m)2 = 0
l2 + m2 - l2 - m2 - 2lm = 0
2lm = 0
Therefore, l = 0 or m = 0
Put l = 0 in (i), we get, n = -m
So, dorection ratios are (l, m, n) = (0, 1, -1)
Put m = 0 in (i), we get, n = -l
So, direction ratios are (l, m, n) = (1, 0, -1)
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