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Ex 11.1, 2 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at August 13, 2026 by Teachoo
Chapter 11 Class 12 Three Dimensional Geometry
Concept wise
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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
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Transcript
Ex 11.1, 2 Find the direction cosines of a line which makes equal angles with the coordinate axes.Direction cosines of a line making, 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 Given the line makes equal angles with the coordinate axes. So, ๐ถ = ๐ท = ๐ธ Direction cosines are l = cos ๐ถ, m = cos ๐ถ, n = cos ๐ถ We know that l2 + m2 + n2 = 1 cos2 ๐ผ + cos2 ๐ฝ + cos2 ๐พ = 1 cos2 ๐ถ + cos2 ๐ถ + cos2 ๐ถ = 1 3 cos2 ๐ผ = 1/3 cos2 ๐ผ = 1/3 cos ๐ผ = ยฑ โ(1/3) โด cos ๐ถ = ยฑ ๐/โ๐ Therefore, direction cosines are l = ยฑ ๐/โ๐, m = ยฑ ๐/โ๐, n = ยฑ ๐/โ๐
