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Misc 4 - Find equation of line parallel to x-axis and passing through

Misc 4 - Chapter 11 Class 12 Three Dimensional Geometry - Part 2

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Misc 4 (Introduction) Find the equation of a line parallel to x-axis and passing through the origin.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 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. Misc 4 Find the equation of a line parallel to x-axis and passing through the origin.Equation of a line passing through (x1, y1, z1) and parallel to a line with direction ratios a, b, c is (𝒙 − 𝒙𝟏)/𝒂 = (𝒚 − 𝒚𝟏)/𝒃 = (𝒛 − 𝒛𝟏)/𝒄 Since line passes through origin ie. (0, 0, 0), x1 = 0, y1 = 0, z1 = 0 Since line is parallel to x – axis, 𝑎 = 1, b = 0, c = 0 Equation of line is (𝑥 − 0)/1 = (𝑦 − 0)/0 = (𝑧 − 0)/0 𝒙/𝟏 = 𝒚/𝟎 = 𝒛/𝟎

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.