Ex 11.1, 2 - Chapter 11 Class 12 Three Dimensional Geometry (Important Question)

Last updated at April 16, 2024 by

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo