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
CBSE Class 12 Sample Paper for 2023 Boards
Last updated at Dec. 13, 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