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 Ex 11.1, 2 - Find direction cosines of a line equal angles - Direction cosines and ratios

Ex 11.1, 2 - Chapter 11 Class 12 Three Dimensional Geometry - Part 2

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Ex 11.1, 2 Find the direction cosines of a line which makes equal angles with the coordinate axes. Direction cosines of a line making, 𝛼 with x – axis, 𝛽 with y – axis, and 𝛾 with z – axis are l, m, n l = cos 𝛼, m = cos 𝛽 , n = cos 𝛾 Given the line makes equal angles with the coordinate axes. So, 𝛼 = 𝛽 = 𝛾 Direction cosines are l = cos 𝛼, m = cos 𝛼, n = cos 𝛼 We know that l2 + m2 + n2 = 1 cos2 𝛼 + cos2 𝛽 + cos2 𝛾 = 1 cos2 𝛼 + cos2 𝛼 + cos2 𝛼 = 1 3 cos2 𝛼 = 1﷮3﷯ cos2 𝛼 = 1﷮3﷯ cos 𝛼 = ± ﷮ 1﷮3﷯﷯ ∴ cos 𝛼 = ± 1﷮ ﷮3﷯﷯ Therefore, direction cosines are l = ± 𝟏﷮ ﷮𝟑﷯﷯ , m = ± 𝟏﷮ ﷮𝟑﷯﷯ , n = ± 𝟏﷮ ﷮𝟑﷯﷯

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.