Last updated at March 11, 2017 by Teachoo

Transcript

Ex 11.2, 15 (Cartesian method) Find the shortest distance between the lines 𝑥 + 17 = 𝑦 + 1 − 6 = 𝑧 + 11 and 𝑥 − 31 = 𝑦 − 5 − 2 = 𝑧 − 71 Shortest distance between two lines l1: 𝑥 − 𝑥1 𝑎1 = 𝑦 − 𝑦1 𝑏1 = 𝑧 − 𝑧1 𝑐1 l2: 𝑥 − 𝑥2 𝑎2 = 𝑦 − 𝑦2 𝑏2 = 𝑧 − 𝑧2 𝑐2 is 𝒙𝟐 − 𝒙𝟏 𝒚𝟐 − 𝒚𝟏 𝒛𝟐 − 𝒛𝟏 𝒂𝟏 𝒃𝟏 𝒄𝟏 𝒂𝟐 𝒃𝟐 𝒄𝟐 𝒂𝟏 𝒃𝟐 − 𝒂𝟐 𝒃𝟏𝟐 + 𝒃𝟏 𝒄𝟐 − 𝒃𝟐 𝒄𝟏𝟐 + 𝒄𝟏 𝒂𝟐 − 𝒄𝟐 𝒂𝟏𝟐 d = 𝑥2− 𝑥1 𝑦2 − 𝑦1 𝑧2 − 𝑧1 𝑎1 𝑏1 𝑐1 𝑎2 𝑏2 𝑐2 𝑎1 𝑏2 − 𝑎2 𝑏12 + 𝑏1 𝑐2 − 𝑏2 𝑐12 + 𝑐1 𝑎2 − 𝑐2 𝑎12 d = 3−(−1)5−(−1)7−(−1)7−611−21 7(−2) −1(−6)2 + −6(1)− −212 + 1(1) −1(7)2 d = 4687−611−21 −14 + 62 + −6 + 22 + 1 − 72 d = 4687−611−21 82 + −42 + −62 d = 4687−611−21 116 d = 4 −6 1− −21−6 7 1−1 1+8 7 −2−1 −6 116 d = 4 −6 + 2−6 7 − 1+8(−14 + 6) 116 d = −16 − 36 − 64 116 d = −116 116 d = − 116 d = 116 d = 4 × 29 d = 𝟐 𝟐𝟗 Ex 11.2, 15 (Vector method) Find the shortest distance between the lines 𝑥 + 17 = 𝑦 + 1 − 6 = 𝑧 + 11 and 𝑥 − 31 = 𝑦 − 5 − 2 = 𝑧 − 71 Shortest distance between two lines 𝑟 = 𝑎1 + λ 𝑏1 and 𝑟 = 𝑎2 + μ 𝑏2 is 𝒃𝟏 × 𝒃𝟐 . 𝒂𝟐 × 𝒂𝟏 𝒃𝟏 × 𝒃𝟐

Shortest distance between two skew 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.