Miscellaneous

Chapter 11 Class 12 Three Dimensional Geometry
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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 