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Question 23 (Choice 2) - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by Teachoo

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

 

Transcript

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
  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

    3. CBSE Class 12 Sample Paper for 2023 Boards

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Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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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