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Example 2 - If a line has direction ratios 2, -1, 2, direction cosines

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

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Example 2 If a line has direction ratios 2, – 1, – 2, determine its direction cosines.If direction ratios of a line are a, b, c direction cosines are π‘Ž/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) , 𝑏/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) , 𝑐/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) Given, Direction ratios = 2, βˆ’1, βˆ’2 ∴ π‘Ž = 2, b = βˆ’1, c = βˆ’2 Also, √(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) = √(22 + (βˆ’1)2 + (βˆ’2)2) = √(4 + 1 + 4) = √9 = 3 Direction cosines = π‘Ž/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) , 𝑏/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) , 𝑐/√(π‘Ž^2 + 𝑏^2 + 𝑐^2 ) = 𝟐/πŸ‘ , (βˆ’πŸ)/πŸ‘ , (βˆ’πŸ)/πŸ‘

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