1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise


Ex 11.1, 1 If a line makes angles 90ยฐ, 135ยฐ, 45ยฐ with the x, y and z โ€“ axes respectively, find its direction cosines. Direction cosines of a line making angle ๐›ผ with x โ€“ axis, ๐›ฝ with y โ€“ axis and ๐›พ with z โ€“ axis are l, m, n l = cos ๐›ผ, m = cos ๐›ฝ, n = cos ๐›พ Here, ๐›ผ = 90ยฐ, ๐›ฝ = 135ยฐ, ๐›พ = 45ยฐ, So, direction cosines are l = cos 90ยฐ = 0 ๐‘š = cosโก135ยฐ = cos(180 โ€“ 45ยฐ) = โ€“cos 45ยฐ = (โˆ’1)/โˆš2 ๐‘› = cos 45ยฐ = 1/โˆš2 Therefore, required direction cosines are 0, ( โˆ’๐Ÿ)/โˆš๐Ÿ , ๐Ÿ/โˆš๐Ÿ .

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.