Ex 11.2, 2 - Show line (1, -1, 2), (3, 4, -2) is perpendicular - Angle between two lines - Direction ratios or cosines

Ex 11.2, 2 - Chapter 11 Class 12 Three Dimensional Geometry - Part 2

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

Transcript

Ex 11.2, 2 Show that the line through the points (1, 1, 2), (3, 4, 2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6). Two lines with direction ratios 1, 1, 1 and 2, 2, 2 are perpendicular to each other if + + = 0 Now, 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 3) + (5 2) + ( 4 4) = 6 + 10 + ( 16) = 16 16 = 0 Therefore the given two lines are perpendicular.

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