Misc 1 - Show line joining origin to (2, 1, 1) is perpendicular - Angle between two lines - Direction ratios or cosines

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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, 1), (4, 3, 1). Two lines having direction ratios 1, 1 , 1 and 2, 2, 2 are Perpendicular to each other if 1 2 + 1 2 + 1 2 = 0 Also, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 x1), (y2 y1), (z2 z1) Now, 1 2 + 1 2 + 1 2 = (2 1) + (1 2) + (1 0) = 2 + ( 2) + 0 = 2 2 = 0 Therefore, the given two lines are perpendicular

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.