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Last updated at Feb. 1, 2020 by Teachoo
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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 ๐ผ with x -axis, ๐ฝ with y โ axis and ๐พ with z โ axis are l, m, n l = cos ๐ผ , m = cos ๐ฝ , n = cos ๐พ x โ axis makes an angle 0ยฐ with x โ axis, 90ยฐ with y โ axis & 90ยฐ with z โ axis. So, ๐ผ = 0ยฐ, ๐ฝ = 90ยฐ, ๐พ = 90ยฐ Direction cosines are l = cos 0ยฐ , m = cos 90ยฐ , n = cos 90ยฐ l = 1 , m = 0, n = 0 โด Direction cosines of x โ 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 (๐ โ ๐๐)/๐ = (๐ โ ๐๐)/๐ = (๐ โ ๐๐)/๐ Since line passes through origin ie. (0, 0, 0), x1 = 0, y1 = 0, z1 = 0 Since line is parallel to x โ axis, ๐ = 1, b = 0, c = 0 Equation of line is (๐ฅ โ 0)/1 = (๐ฆ โ 0)/0 = (๐ง โ 0)/0 ๐/๐ = ๐/๐ = ๐/๐
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