Ex 11.1, 3 - Chapter 11 Class 12 Three Dimensional Geometry

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Ex 11.1, 3 If a line has the direction ratios −18, 12, −4, then what are 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 = −18, 12, −4 𝒂 = −18, b = 12, c = −4 And, √(𝒂𝟐+𝒃𝟐+𝒄𝟐) = √((−18)2+122+(−4)2) √(𝒂𝟐+𝒃𝟐+𝒄𝟐) = √((−18)2+122+(−4)2) = √(324+144+16) = √484 = 22 Therefore, Direction cosines = 𝑎/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) , 𝑏/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) , 𝑐/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) = (−18)/22 , 12/22 , (−4)/22 = (−𝟗)/𝟏𝟏 , 𝟔/𝟏𝟏 , (−𝟐)/𝟏𝟏