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

Last updated at December 16, 2024 by Teachoo

Ex 11.1, 2 - Find direction cosines of a line which make equal angles - Ex 11.1

part 2 - Ex 11.1, 2 - Ex 11.1 - Serial order wise - Chapter 11 Class 12 Three Dimensional Geometry

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Transcript

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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