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Example, 5 - Chapter 11 Class 12 Three Dimensional Geometry (Term 2)

Last updated at March 22, 2023 by

Example 5 - Show A (2, 3, -4), B (1, -2, 3), C (3, 8, -11)

Example, 5 - Chapter 11 Class 12 Three Dimensional Geometry - Part 2

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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 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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