Ex 11.1, 1 - If a line makes 90, 135, 45 with x, y, z-axes - Direction cosines and ratios

  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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Ex 11.1, 1 If a line makes angles 90° , 135°, 45° with the x, y and z – axes 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 = 135° , 𝛾 = 45° , So, direction cosines are l = cos 90° = 0 𝑚 = cos﷮135﷯° = cos(180 – 45°) = –cos 45° = −1﷮ ﷮2﷯﷯ 𝑛 = cos 45° = 1﷮ ﷮2﷯﷯ Therefore, required direction cosines are 0, −𝟏﷮ ﷮𝟐﷯﷯ , 𝟏﷮ ﷮𝟐﷯﷯ .

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