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Example 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
-
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
Example 1 If a line makes angle 90°, 60° and 30° with the positive direction of x, y and z-axis 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 = 60° , 𝛾 = 30° So, direction cosines of the line are l = cos 90° , m = cos60° , n = cos 30° l = 0 , m = 1/2 , n = √3/2 Therefore, direction cosines are 0, 𝟏/𝟐, √𝟑/𝟐
