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


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Example 5 Show that the points A (2, 3, – 4), B (1, – 2, 3) and C (3, 8, – 11) are collinear. Three points A, B, C are collinear if direction ratios of AB and BC are proportional. AB A (2, 3, −4) B (1, −2, 3) Direction ratios = 1 − 2, −2 − 3, 3 − (−4) = −1, −5, 7 So, 𝑎1, = −1 , b1 = −5, c1 = 7 BC B (1, −2, 3) C (3, 8, −11) Direction ratios = 3 − 1, 8 − (−2), −11 − 3 = 2, 10, −14 So, 𝑎2, = 2 , b2 = 10, c2 = −14 Now, 𝒂𝟐/𝒂𝟏 = 2/( −1) = –2 𝒃𝟐/𝒃𝟏 = 10/( −5) = –2 𝒄𝟐/𝒄𝟏 = ( − 14)/7 = –2 Since, 𝒂𝟐/𝒂𝟏 = 𝒃𝟐/𝒃𝟏 = 𝒄𝟐/𝒄𝟏 = −2 Therefore, 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.