Find the direction ratio and direction cosines of a line parallel to the line whose equations are 6𝑥 − 12 = 3𝑦 + 9 = 2𝑧 − 2
CBSE Class 12 Sample Paper for 2023 Boards
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CBSE Class 12 Sample Paper for 2023 Boards
Last updated at April 16, 2024 by Teachoo
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