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

Transcript

Misc 1 Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, โ€“ 1), (4, 3, โ€“ 1).Two lines having direction ratios ๐‘Ž1, ๐‘1 , ๐‘1 and ๐‘Ž2, ๐‘2, ๐‘2 are Perpendicular to each other if ๐’‚1 ๐’‚2 + ๐’ƒ1 ๐’ƒ2 + ๐’„1 ๐’„2 = 0 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 (0, 0, 0) B (2, 1, 1) Direction ratios : (2 โˆ’ 0), (1 โˆ’ 0), (1 โˆ’ 0) = 2, 1, 1 โˆด ๐’‚1 = 2, ๐’ƒ1 = 1, ๐’„1 = 1 C (3, 5, โˆ’1) D (4, 3, โˆ’1) Direction ratios: (4 โˆ’ 3), (3 โˆ’ 5), ( โˆ’1 + 1) = 1, โˆ’2, 0 โˆด ๐’‚2 = 1, ๐’ƒ2 = โˆ’2, ๐’„2 = 0 Now, ๐‘Ž1 ๐‘Ž2 + ๐‘1 ๐‘2 + ๐‘1 ๐‘2 = (2 ร— 1) + (1 ร— โˆ’2) + (1 ร— 0) = 2 + (โˆ’2) + 0 = 2 โˆ’ 2 = 0 Therefore, the given two lines are perpendicular

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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.