Example, 2 - Chapter 11 Class 12 Three Dimensional Geometry

Last updated at April 16, 2024 by Teachoo

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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 𝒂/√(𝒂^𝟐 + 𝒃^𝟐 + 𝒄^𝟐 ) , 𝒃/√(𝒂^𝟐 + 𝒃^𝟐 + 𝒄^𝟐 ) , 𝒄/√(𝒂^𝟐 + 𝒃^𝟐 + 𝒄^𝟐 ) Given, Direction ratios = 2, −1, −2 ∴ 𝑎 = 2, b = −1, c = −2 Also, √(𝒂^𝟐 + 𝒃^𝟐 + 𝒄^𝟐 ) = √(22 + (−1)2 + (−2)2) = √(4 + 1 + 4) = √9 = 3 Direction cosines = 𝑎/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) , 𝑏/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) , 𝑐/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) = 𝟐/𝟑 , (−𝟏)/𝟑 , (−𝟐)/𝟑

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