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Angle between the pair of lines (๐ฅ โ ๐ฅ1)/๐1 = (๐ฆ โ ๐ฆ1)/๐1 = (๐ง โ ๐ง1)/๐1 and (๐ฅ โ ๐ฅ2)/๐2 = (๐ฆ โ ๐ฆ2)/๐2 = (๐ง โ ๐ง2)/๐2 is given by cos ฮธ = |(๐_๐ ๐_๐ + ๐_๐ ๐_๐ +ใ ๐ใ_๐ ๐_๐)/(โ(ใ๐_๐ใ^๐ + ใ๐_๐ใ^๐+ ใ๐_๐ใ^๐ ) โ(ใ๐_๐ใ^๐ +ใใ ๐ใ_๐ใ^๐+ ใ๐_๐ใ^๐ ))| ๐/๐ = ๐/๐ = ๐/๐ (๐ฅ โ 0)/2 = (๐ฆ โ 0)/2 = (๐ง โ 0)/1 Comparing with (๐ฅ โ ๐ฅ1)/๐1 = (๐ฆ โ ๐ฆ1)/๐1 = (๐ง โ ๐ง1)/๐1 x1 = 0, y1 = 0, z1 = 0 & ๐1 = 2, b1 = 2, c1 = 1 (๐ โ ๐)/๐ = (๐ โ ๐)/๐ = (๐ โ ๐)/๐ Comparing with (๐ฅ โ ๐ฅ2)/๐2 = (๐ฆ โ ๐ฆ2)/๐2 = (๐ง โ ๐ง2)/๐2 ๐ฅ2 = 5, y2 = 2, z2 = 5 & ๐2 = 4, ๐2 = 1, ๐2 = 8 Now, cos ฮธ = |(๐_๐ ๐_๐ + ๐_๐ ๐_๐ +ใ ๐ใ_๐ ๐_๐)/(โ(ใ๐_๐ใ^๐ + ใ๐_๐ใ^๐+ ใ๐_๐ใ^๐ ) โ(ใ๐_๐ใ^๐ +ใใ ๐ใ_๐ใ^๐+ ใ๐_๐ใ^๐ ))| = |((2 ร 4) + (2 ร 1) + (1 ร 8) )/(โ(22 + 22 + 12) ร โ(42 + 12 + 82))| = |(8 + 2 + 8 )/(โ(4 + 4 + 1) โ(16 + 1 + 64))| = |18/(โ9 ร โ81)| = 18/(3 ร 9) = 2/3 So, cos ฮธ = 2/3 โด ฮธ = cos-1 (๐/๐) Therefore, the angle between the given lines is cosโ1(๐/๐).

Ex 11.2

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Ex 11.2, 10 (i) Important Deleted for CBSE Board 2022 Exams

Ex 11.2, 10 (ii)

Ex 11.2, 11 (i) Important Deleted for CBSE Board 2022 Exams

Ex 11.2, 11 (ii) You are here

Ex 11.2, 12 Important

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Chapter 11 Class 12 Three Dimensional Geometry (Term 2)

Serial order wise

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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.