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Example, 3 - Chapter 11 Class 12 Three Dimensional Geometry

Last updated at Aug. 14, 2023 by

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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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.