Ex 11.2, 13 - Show lines are perpendicular to each other. - Ex 11.2

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  1. Chapter 11 Class 12 Three Dimensional Geometry
  2. Serial order wise
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Ex 11.2, 13 Show that the lines 𝑥 − 5﷮7﷯ = 𝑦 + 2﷮ −5﷯ = 𝑧﷮1﷯ and 𝑥﷮1﷯ = 𝑦﷮2﷯ = 𝑧﷮3﷯ are perpendicular to each other. Two lines 𝑥 − 𝑥1﷮𝑎1﷯ = 𝑦 − 𝑦1﷮𝑏1﷯ = 𝑧 − 𝑧1﷮𝑐1﷯ and 𝑥 − 𝑥2﷮𝑎2﷯ = 𝑦 − 𝑦2﷮𝑏2﷯ = 𝑧 − 𝑧2﷮𝑐2﷯ are perpendicular to each other if 𝒂𝟏 𝒂𝟐 + 𝒃𝟏 𝒃𝟐 + 𝒄𝟏 𝒄𝟐 = 0 So, 𝑎1 𝑎2 + 𝑏1 𝑏2 + 𝑐1 𝑐2 = (7 × 1) + (−5 × 2) + (1 × 3) = 7 + (−10) + 3 = 0 Therefore, the two given lines are perpendicular to each other.

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