Misc 4

Transcript

Misc 4 (Introduction) Find the equation of a line parallel to x-axis and passing through the origin. 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 : 𝑥 − 0﷮1﷯ = 𝑦 − 0﷮0﷯ = 𝑧 − 0﷮0﷯ 𝒙﷮𝟏﷯ = 𝒚﷮𝟎﷯ = 𝒛﷮𝟎﷯