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Ex 11.1, 1 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at Dec. 16, 2024 by Teachoo
Chapter 11 Class 12 Three Dimensional Geometry
Concept wise
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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
Transcript
Ex 11.1, 1 If a line makes angles 90°, 135°, 45° with the x, y and z – axes respectively, find its direction cosines. Direction cosines of a line making angle 𝛼 with x – axis, 𝛽 with y – axis and 𝛾 with z – axis are l, m, n l = cos 𝜶, m = cos 𝜷, n = cos 𝜸 Here, 𝛼 = 90°, 𝛽 = 135°, 𝛾 = 45°, So, direction cosines are l = cos 90° 𝒎 = cos 135° 𝒏 = cos 45° = cos (180 – 45°) = –cos 45° = (−𝟏)/√𝟐 = 𝟏/√𝟐 Therefore, required direction cosines are 0, ( −𝟏)/√𝟐 , 𝟏/√𝟐 .
