Last updated at May 29, 2018 by Teachoo

Transcript

Example 21 Show that the lines + 3 3 = 1 1 = 5 5 and + 1 1 = 2 2 = 5 5 are coplanar. Two lines 1 1 = 1 1 = 1 1 and 2 2 = 2 2 = 2 2 are coplanar if = 0 Given, the two lines are Now, 2 1 2 1 2 1 1 1 1 2 2 2 = 1 ( 3) 2 1 5 5 3 1 5 1 2 5 = 2 1 0 3 1 5 1 2 5 = 2 1 5 (2 5) 1 3 5 ( 1 5) + 0 3 2 ( 1 1) = 2 5 10 1 15 ( 5) + 0 = 2( 5) 1( 10) = 10 + 10 = 0 Therefore, the given two lines are coplanar.

Coplanarity of 2 lines

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.