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Find the direction cosines of the following line: (3 βˆ’ π‘₯)/(βˆ’1) = (2𝑦 βˆ’ 1)/2 = 𝑧/4

This question is similar to Question 4 or 2nd CBSE Class 12 Sample Paper 2019 BoardsΒ 

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Transcript

Question 4 Find the direction cosines of the following line: (3 βˆ’ π‘₯)/(βˆ’1) = (2𝑦 βˆ’ 1)/2 = 𝑧/4 Given line (πŸ‘ βˆ’ 𝒙)/(βˆ’πŸ) = (2𝑦 βˆ’ 1)/2 = 𝑧/4 (βˆ’(π‘₯ βˆ’ 3) )/(βˆ’1) = (2𝑦 βˆ’ 1)/2 = 𝑧/4 ((𝒙 βˆ’ πŸ‘) )/𝟏 = (2𝑦 βˆ’ 1)/2 = 𝑧/4 ((π‘₯ βˆ’ 3) )/1 = 𝟐(π’š βˆ’ Β½)/𝟐 = 𝑧/4 ((π‘₯ βˆ’ 3) )/1 = ((π’š βˆ’ Β½))/𝟏 = 𝑧/4 So, direction ratios are 1, 1, 4 Β½ marks ∴ a = 1, b = 1, c = 4 Direction cosines = 1/√(1^2 + 1^2 + 4^2 ) , 1/√(1^2 + 1^2 + 4^2 ) , 4/√(1^2 + 1^2 + 4^2 ) = 1/√(1 + 1 + 16) ,1/√(1 + 1 + 16) ,4/√(1 + 1 + 16) = 1/√18 ,1/√18 ,4/√18 = 1/√(2 Γ— 9) ,1/√(2 Γ— 9) ,4/√(2 Γ— 9) = 𝟏/(πŸ‘βˆšπŸ) , 𝟏/(πŸ‘βˆšπŸ) , πŸ’/(πŸ‘βˆšπŸ) Β½ marks

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.