You are here
Ex 11.2, 2 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at August 8, 2026 by Teachoo
Angle between two lines - Direction ratios or cosines
Chapter 11 Class 12 Three Dimensional Geometry
Concept wise
- Direction cosines and ratios
- Equation of line - given point and //vector
- Equation of line - given 2 points
- Angle between two lines - Vector
- Angle between two lines - Cartisian
-
Angle between two lines - Direction ratios or cosines
- Shortest distance between two skew lines
- Shortest distance between two parallel lines
- Equation of plane - In Normal Form
- Equation of plane - Prependicular to Vector & Passing Through Point
- Equation of plane - Passing Through 3 Non Collinear Points
- Equation of plane - Intercept Form
- Equation of plane - Passing Through Intersection Of Planes
- Coplanarity of 2 lines
- Angle between two planes
- Distance of point from plane
- Angle between Line and Plane
- Equation of line under planes condition
- Point with Lines and Planes
Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 3 questions, selected from your answers, mistakes, and progress.
Transcript
Ex 11.2, 2 Show that the line through the points (1, โ1, 2), (3, 4, โ2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6). Two lines with direction ratios ๐1, ๐1, ๐1 and ๐2, ๐2, ๐2 are perpendicular to each other if ๐๐ ๐๐ + ๐๐ ๐๐ + ๐๐ ๐๐ = 0 Now, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 โ x1), (y2 โ y1), (z2 โ z1) A (1, โ1, 2) B (3, 4, โ2) Direction ratios (3 โ 1), 4 โ (โ1), โ2 โ 2 = 2, 5, โ4 โด ๐๐ = 2, ๐๐ = 5, ๐๐ = โ4 C (0, 3, 2) D (3, 5, 6) Direction ratios (3 โ 0), (5 โ 3), (6 โ 2) = 3, 2, 4 โด ๐๐ = 3, ๐๐ = 2, ๐๐ = 4 Now, ๐๐ ๐๐ + ๐๐ ๐๐ + ๐๐ ๐๐ = (2 ร 3) + (5 ร 2) + (โ4 ร 4) = 6 + 10 + (โ16) = 16 โ 16 = 0 Therefore the given two lines are perpendicular.
