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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.