Example 18 - Find vector equations of plane passing through - Examples

Slide2.JPG

Slide3.JPG

  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
Ask Download

Transcript

Example 18 (Introduction) Find the vector equations of the plane passing through the points R(2, 5, – 3), S(– 2, – 3, 5) and T(5, 3,– 3). Vector equation of a plane passing through three points with position vectors 𝑎īˇ¯, 𝑏īˇ¯, 𝑐īˇ¯ is ( rīˇ¯ − 𝑎īˇ¯) . ( 𝑏īˇ¯âˆ’ 𝑎īˇ¯)×( 𝑐īˇ¯âˆ’ 𝑎īˇ¯)īˇ¯ = 0 Example 18 Find the vector equations of the plane passing through the points R(2, 5, – 3), S(– 2, – 3, 5) and T(5, 3,– 3). Vector equation of a plane passing through three points with position vectors 𝑎īˇ¯, 𝑏īˇ¯, 𝑐īˇ¯ is ( rīˇ¯ − 𝒂īˇ¯) . ( 𝒃īˇ¯âˆ’ 𝒂īˇ¯)×( 𝒄īˇ¯âˆ’ 𝒂īˇ¯)īˇ¯ = 0 Now the planes passes through the points ( 𝒄īˇ¯ − 𝒂īˇ¯) = (5 𝑖īˇ¯ + 3 𝑗īˇ¯ − 3 𝑘īˇ¯) − (2 𝑖īˇ¯ + 5 𝑗īˇ¯ − 3 𝑘īˇ¯) = (5 − 2) 𝑖īˇ¯ + (3 − 5) 𝑗īˇ¯ + (3 − (− 3)) 𝑘īˇ¯ = 3 𝑖īˇ¯ − 2 𝑗īˇ¯ + 0 𝑘īˇ¯ = 3 𝒊īˇ¯ − 2 𝒋īˇ¯ Vector equation is ( rīˇ¯ − 𝑎īˇ¯) . ( 𝑏īˇ¯âˆ’ 𝑎īˇ¯)×( 𝑐īˇ¯âˆ’ 𝑎īˇ¯)īˇ¯ = 0 ( 𝒓īˇ¯ − (2 𝒊īˇ¯ + 5 𝒋īˇ¯ − 3 𝒌īˇ¯)). −4 𝒊īˇ¯ − 8 𝒋īˇ¯ + 8 𝒌īˇ¯ īˇ¯ × 3 𝒊īˇ¯ − 2 𝒋īˇ¯īˇ¯īˇ¯ = 0

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.