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Example 3  - Find direction cosines of line passing through - Examples

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