You are here
Ex 11.1, 1 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at August 13, 2026 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
Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 3 questions, selected from your answers, mistakes, and progress.
Transcript
Ex 11.1, 1 If a line makes angles 90ยฐ, 135ยฐ, 45ยฐ with the x, y and z โ axes respectively, find its direction cosines. Direction cosines of a line making angle ๐ผ with x โ axis, ๐ฝ with y โ axis and ๐พ with z โ axis are l, m, n l = cos ๐ถ, m = cos ๐ท, n = cos ๐ธ Here, ๐ผ = 90ยฐ, ๐ฝ = 135ยฐ, ๐พ = 45ยฐ, So, direction cosines are l = cos 90ยฐ ๐ = cos 135ยฐ ๐ = cos 45ยฐ = cos (180 โ 45ยฐ) = โcos 45ยฐ = (โ๐)/โ๐ = ๐/โ๐ Therefore, required direction cosines are 0, ( โ๐)/โ๐ , ๐/โ๐ .
