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

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  1. Chapter 11 Class 12 Three Dimensional Geometry
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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. 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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