Find the direction ratio and direction cosines of a line parallel to the line whose equations are 6𝑥 − 12 = 3𝑦 + 9 = 2𝑧 − 2

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Question 23 (Choice 2) Find the direction ratio and direction cosines of a line parallel to the line whose equations are 6𝑥 − 12 = 3𝑦 + 9 = 2𝑧 − 2 Given equation of line 6𝑥 − 12 = 3𝑦 + 9 = 2𝑧 − 2 6(𝑥 − 2) = 3(𝑦 + 3) = 2(𝑧 − 1) Dividing both sides by 6 (6(𝑥 − 2))/6=(3(𝑦 + 3))/6=(2(𝑧 − 1))/6 ((𝒙 − 𝟐))/𝟏=((𝒚 + 𝟑))/𝟐=((𝒛 − 𝟏))/𝟑 Thus, Direction ratios of the line parallel to the line = 1, 2, 3 ∴ 𝑎 = 1, b = 2, c = 3 Also, √(𝒂^𝟐 + 𝒃^𝟐 + 𝒄^𝟐 ) = √(12 +22 +32) = √(1 +4 +9) = √𝟏𝟒 Direction cosines = 𝑎/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) , 𝑏/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) , 𝑐/√(𝑎^2 + 𝑏^2 + 𝑐^2 ) = 𝟏/√𝟏𝟒 , 𝟐/√𝟏𝟒 , 𝟑/√𝟏𝟒

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo