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Ex 11.1, 4 Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear. B(–1, –2, 1) A(2, 3, 4) C(5, 8, 7) Three points A, B, C are collinear if direction ratios of AB and BC are proportional. AB A (2, 3, 4) B (–1, –2, 1) Direction ratios = –1 − 2, –2 −3, 1 − 4 = –3, −5, –3 So, 𝑎1, = −3 , b1 = −5, c1 = –3 BC B (–1, –2, 1) C (5, 8, 7) Direction ratios = 5 − (–1), 8 − (−2), 7 –1 = 6, 10, 6 So, 𝑎2, = 6 , b2 = 10, c2 = 6 Now, 𝒂𝟐/𝒂𝟏 = 6/( −3) = –2 𝒃𝟐/𝒃𝟏 = 10/( −5) = –2 𝒄𝟐/𝒄𝟏 = 6/(−3) = –2 Since, 𝒂𝟐/𝒂𝟏 = 𝒃𝟐/𝒃𝟏 = 𝒄𝟐/𝒄𝟏 = −2 Since direction ratios of AB and BC are proportional ∴ Points A, B and C are collinear.

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo