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Last updated at May 29, 2018 by Teachoo

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 with x- axis, with y- axis and with z axis are l, m, n. l = cos , m = cos , n = cos Here, = 90 , = 60 , = cos 30 So, direction cosines of the line are l = cos 90 , m = cos 60 , n = cos 30 l = 0 , m = 1 2 , n = 3 2 Therefore, direction cosines are 0, ,

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

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.