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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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.

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Davneet Singh

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.