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Ex 11.1, 3 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at August 13, 2026 by Teachoo
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
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Transcript
Ex 11.1, 3 If a line has the direction ratios โ18, 12, โ4, then what are its direction cosines?If direction ratios of a line are a, b, c direction cosines are ๐/โ(๐^๐ + ๐^๐ + ๐^๐ ) , ๐/โ(๐^๐ + ๐^๐ + ๐^๐ ) , ๐/โ(๐^๐ + ๐^๐ + ๐^๐ ) Given, Direction ratios = โ18, 12, โ4 ๐ = โ18, b = 12, c = โ4 And, โ(๐๐+๐๐+๐๐) = โ((โ18)2+122+(โ4)2) โ(๐๐+๐๐+๐๐) = โ((โ18)2+122+(โ4)2) = โ(324+144+16) = โ484 = 22 Therefore, Direction cosines = ๐/โ(๐^2 + ๐^2 + ๐^2 ) , ๐/โ(๐^2 + ๐^2 + ๐^2 ) , ๐/โ(๐^2 + ๐^2 + ๐^2 ) = (โ18)/22 , 12/22 , (โ4)/22 = (โ๐)/๐๐ , ๐/๐๐ , (โ๐)/๐๐
