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Example 1 - If line makes angle 90, 60, 30 with x, y, z-axis - Direction cosines and ratios

  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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Example 1 If a line makes angle 90°, 60° and 30° with the positive direction of x, y and z-axis respectively, find its direction cosines. Direction cosines of a line making angle 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 Here, 𝛼 = 90° , 𝛽 = 60° , 𝛾 = cos 30° So, direction cosines of the line are l = cos 90° , m = cos﷮60﷯° , n = cos 30° l = 0 , m = 1﷮2﷯ , n = ﷮3﷯﷮2﷯ Therefore, direction cosines are 0, 𝟏﷮𝟐﷯, ﷮𝟑﷯﷮𝟐﷯

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