web analytics

Ex 11.2, 3 - Show line (4, 7, 8), (2, 3, 4) is parallel to - Angle between two lines - Direction ratios or cosines

Slide7.JPG

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

Transcript

Ex 11.2, 3 Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (–1, –2, 1), (1, 2, 5). Two lines having direction ratios 𝑎1, b1, c1 and 𝑎2, b2, c2 are parallel if 𝒂𝟏﷮𝒂𝟐﷯ = 𝒃𝟏﷮𝒃𝟐﷯ = 𝒄𝟏﷮𝒄𝟐﷯ Also, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 − x1), (y2 − y1), (z2 − z1) Now, 𝑎1﷮𝑎2﷯ = −2﷮2﷯ = –1, 𝑏1﷮𝑏2﷯ = −4﷮4﷯ = –1 𝑐1﷮𝑐2﷯ = −4﷮4﷯ = –1 Since 𝑎1﷮𝑎2﷯ = 𝑏1﷮𝑏2﷯ = 𝑐1﷮𝑐2﷯ = −1, Therefore, the given lines are parallel.

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