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Example 4 - Find direction cosines of x, y, z-axis - Class 12 - Direction cosines and ratios


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  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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Example, 4 Find the direction cosines of x, y and z-axis. x – axis makes an angle 0° with x – axis, 90° with y – axis & 90° with z – axis. So, 𝛼 = 0° , 𝛽 = 90° , 𝛾 = 90° Direction cosines are l = cos 0° , m = cos 90° , n = cos 90° l = 1 , m = 0, n = 0 ∴ Direction cosines of x – axis are 1, 0, 0. y– axis makes an angle 90° with x – axis, 0° with y – axis & 90° with z – axis. So, 𝛼 = 90° , 𝛽 = 0° , 𝛾 = 90° Direction cosines are l = cos 90° , m = cos 0° , n = cos 90° l = 0 , m = 1, n = 0 ∴ Direction cosines of y – axis are 0, 1, 0. z– axis makes an angle 90° with x – axis, 90° with y – axis & 0° with z – axis. So, 𝛼 = 90° , 𝛽 = 90° , 𝛾 = 0° Direction cosines are l = cos 90° , m = cos 90° , n = cos 0° l = 0 , m = 0, n = 1 ∴ Direction cosines of z – axis are 0, 0, 1.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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