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

Transcript

Ex 11.2, 3 Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (โ€“1, โ€“2, 1), (1, 2, 5).Two lines having direction ratios ๐‘Ž1, b1, c1 and ๐‘Ž2, b2, c2 are parallel if ๐’‚๐Ÿ/๐’‚๐Ÿ = ๐’ƒ๐Ÿ/๐’ƒ๐Ÿ = ๐’„๐Ÿ/๐’„๐Ÿ Also, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 โˆ’ x1), (y2 โˆ’ y1), (z2 โˆ’ z1) A (4, 7, 8), B (2, 3, 4) Direction ratios = 2 โˆ’ 4, 3 โˆ’ 7, 4 โˆ’ 8 = โˆ’2, โˆ’4, โˆ’4 โˆด ๐’‚๐Ÿ = โˆ’2, ๐’ƒ๐Ÿ = โˆ’4, ๐’„๐Ÿ = โˆ’4 C (โˆ’1, โˆ’2, 1), D (1, 2, 5) Direction ratios = 1 โˆ’ (โˆ’1), 2 โˆ’ (โˆ’2), 5 โˆ’ 1 = 2, 4, 4 โˆด ๐’‚๐Ÿ = 2, ๐’ƒ๐Ÿ = 4, ๐’„๐Ÿ = 4 Now, ๐‘Ž1/๐‘Ž2 = (โˆ’2)/2 = โ€“1 ๐‘1/๐‘2 = (โˆ’4)/4 = โ€“1 ๐‘1/๐‘2 = (โˆ’4)/4 = โ€“1 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 = ๐‘1/๐‘2 = โˆ’1 Therefore, the given lines are parallel.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.