web analytics

Example 21 - Show that lines x+3/3 = y-1/1 = z-5/5 are coplanar - Examples

Slide11.JPG

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

Transcript

Example 21 Show that the lines 𝑥 + 3﷮ − 3﷯ = 𝑦 − 1﷮1﷯ = 𝑧 − 5﷮5﷯ and 𝑥 + 1﷮ − 1﷯ = 𝑦 − 2﷮2﷯ = 𝑧 − 5﷮5﷯ are coplanar. Two lines 𝑥 − 𝑥﷮1﷯﷮ 𝑎﷮1﷯﷯ = 𝑦 − 𝑦﷮1﷯﷮ 𝑏﷮1﷯﷯ = 𝑧 − 𝑧﷮1﷯﷮ 𝑐﷮1﷯﷯ and 𝑥 − 𝑥﷮2﷯﷮ 𝑎﷮2﷯﷯ = 𝑦 − 𝑦﷮2﷯﷮ 𝑏﷮2﷯﷯ = 𝑧 − 𝑧﷮2﷯﷮ 𝑐﷮2﷯﷯ are coplanar if 𝒙﷮𝟐﷯− 𝒙﷮𝟏﷯﷮ 𝒚﷮𝟐﷯− 𝒚﷮𝟏﷯﷮ 𝒛﷮𝟐﷯− 𝒛﷮𝟏﷯﷮ 𝒂﷮𝟏﷯﷮ 𝒃﷮𝟏﷯﷮ 𝒄﷮𝟏﷯﷮ 𝒂﷮𝟐﷯﷮ 𝒃﷮𝟐﷯﷮ 𝒄﷮𝟐﷯﷯﷯ = 0 Given, the two lines are Now, 𝑥﷮2﷯− 𝑥﷮1﷯﷮ 𝑦﷮2﷯− 𝑦﷮1﷯﷮ 𝑧﷮2﷯− 𝑧﷮1﷯﷮ 𝑎﷮1﷯﷮ 𝑏﷮1﷯﷮ 𝑐﷮1﷯﷮ 𝑎﷮2﷯﷮ 𝑏﷮2﷯﷮ 𝑐﷮2﷯﷯﷯ = −1−(−3)﷮2−1﷮5−5﷮ −3﷮1﷮5﷮ −1﷮2﷮5﷯﷯ = 2﷮1﷮0﷮ −3﷮1﷮5﷮ −1﷮2﷮5﷯﷯ = 2 1×5﷯− (2×5)﷯ − 1 − 3×5﷯−(− 1×5)﷯ + 0 − 3×2﷯−(− 1×1)﷯ = 2 5−10﷯− 1 − 15−(− 5)﷯ + 0 = 2(−5) −1(−10) = −10 + 10 = 0 Therefore, the given two lines are coplanar.

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 provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail