1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
  3. Examples
Check sibling questions

Example, 3 - Chapter 11 Class 12 Three Dimensional Geometry

Last updated at Dec. 16, 2024 by Teachoo

Transcript

Example 3 Find the direction cosines of the line passing through the two points (– 2, 4, – 5) and (1, 2, 3). Direction ratios of a line passing through two points P(x1, y1, z1,), & Q (x2, y2, z2) = (x2 – x1), (y2 − y1), (z2 − z1) Direction cosines = (𝒙𝟐 − 𝒙𝟏)/𝑷𝑸 , (𝒚𝟐 − 𝒚𝟏)/𝑷𝑸 , (𝒛𝟐 − 𝒛𝟏)/𝑷𝑸 where, PQ = √((𝑥2 − 𝑥1)^2 + (𝑦2 − 𝑦1)^2 + (𝑧2 − 𝑧1)^2 ) Given P (−2, 4, − 5) & Q (1, 2, 3) So, x1 = −2, y1 = 4, z1 = −5 & x2 = 1, y2 = 2, z2 = 3 Direction ratios = (x2 – x1), (y2 − y1), (z2 − z1) = 1 − (−2), 2 − 4, 3 − (−5) = 1 + 2, −2, 3 + 5 = 3, −2, 8 Direction cosines = 3/√(32 + (−2)2 + 82) , ( −2)/√(32 + (−2)2 + 82) , 8/√(32 + (−2)2 + 82) = 3/√(9 + 4 + 64) , ( −2)/√(9 + 4 + 64) , 8/√(9 + 4 + 64) = 𝟑/√𝟕𝟕 , ( −𝟐)/√𝟕𝟕 , 𝟖/√𝟕𝟕
  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise

    3. Examples

    Miscellaneous →
Miscellaneous →
Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

About the Author

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo