Last updated at Dec. 19, 2018 by Teachoo

Transcript

Example, 4 Find the direction cosines of x, y and z-axis. x axis makes an angle 0 with x axis, 90 with y axis & 90 with z axis. So, = 0 , = 90 , = 90 Direction cosines are l = cos 0 , m = cos 90 , n = cos 90 l = 1 , m = 0, n = 0 Direction cosines of x axis are 1, 0, 0. y axis makes an angle 90 with x axis, 0 with y axis & 90 with z axis. So, = 90 , = 0 , = 90 Direction cosines are l = cos 90 , m = cos 0 , n = cos 90 l = 0 , m = 1, n = 0 Direction cosines of y axis are 0, 1, 0. z axis makes an angle 90 with x axis, 90 with y axis & 0 with z axis. So, = 90 , = 90 , = 0 Direction cosines are l = cos 90 , m = cos 90 , n = cos 0 l = 0 , m = 0, n = 1 Direction cosines of z axis are 0, 0, 1.

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.