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Ex 11.2

Ex 11.2, 1

Ex 11.2, 2 You are here

Ex 11.2, 3 Important

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Ex 11.2, 8 (i) Important

Ex 11.2, 8 (ii)

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Ex 11.2, 9 (ii)

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Question 1 Important Deleted for CBSE Board 2024 Exams

Question 2 Deleted for CBSE Board 2024 Exams

Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

Last updated at Aug. 14, 2023 by Teachoo

Ex 11.2, 2 Show that the line through the points (1, −1, 2), (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6). Two lines with direction ratios 𝑎1, 𝑏1, 𝑐1 and 𝑎2, 𝑏2, 𝑐2 are perpendicular to each other if 𝒂𝟏 𝒂𝟐 + 𝒃𝟏 𝒃𝟐 + 𝒄𝟏 𝒄𝟐 = 0 Now, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 − x1), (y2 − y1), (z2 − z1) A (1, −1, 2) B (3, 4, −2) Direction ratios (3 − 1), 4 − (−1), −2 − 2 = 2, 5, –4 ∴ 𝒂𝟏 = 2, 𝒃𝟏 = 5, 𝒄𝟏 = −4 C (0, 3, 2) D (3, 5, 6) Direction ratios (3 − 0), (5 − 3), (6 − 2) = 3, 2, 4 ∴ 𝒂𝟐 = 3, 𝒃𝟐 = 2, 𝒄𝟐 = 4 Now, 𝒂𝟏 𝒂𝟐 + 𝒃𝟏 𝒃𝟐 + 𝒄𝟏 𝒄𝟐 = (2 × 3) + (5 × 2) + (−4 × 4) = 6 + 10 + (−16) = 16 − 16 = 0 Therefore the given two lines are perpendicular.