Ex 11.2
Ex 11.2, 2 You are here
Ex 11.2, 3 Important
Ex 11.2, 4
Ex 11.2, 5 Important
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Ex 11.2, 7 Important
Ex 11.2, 8 (i) Important
Ex 11.2, 8 (ii)
Ex 11.2, 9 (i) Important
Ex 11.2, 9 (ii)
Ex 11.2, 10 Important
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Ex 11.2, 12 Important
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Ex 11.2, 15 Important
Question 1 Important Deleted for CBSE Board 2024 Exams
Question 2 Deleted for CBSE Board 2024 Exams
Last updated at April 16, 2024 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.