You are here
Ex 11.2, 4 - Chapter 11 Class 12 Three Dimensional Geometry
Last updated at April 16, 2024 by Teachoo
Equation of line - given point and //vector
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
Transcript
Ex 11.2, 4 Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3𝑖 ̂ + 2𝑗 ̂ – 2𝑘 ̂ . Equation of a line passing through a point with position vector 𝑎 ⃗, and parallel to a vector 𝑏 ⃗ is 𝒓 ⃗ = 𝒂 ⃗ + 𝜆𝒃 ⃗ Since line passes through (1, 2, 3) 𝒂 ⃗ = 1𝒊 ̂ + 2𝒋 ̂ + 3𝒌 ̂ Since line is parallel to 3𝑖 ̂ + 2𝑗 ̂ − 2𝑘 ̂ 𝒃 ⃗ = 3𝒊 ̂ + 2𝒋 ̂ − 2𝒌 ̂ Equation of line 𝑟 ⃗ = 𝑎 ⃗ + 𝜆𝑏 ⃗ 𝒓 ⃗ = (𝒊 ̂ + 2𝒋 ̂ + 3𝒌 ̂) + 𝜆 (3𝒊 ̂ + 2𝒋 ̂ − 2𝒌 ̂)
