Find the direction cosines of the following line:(3 − 𝑥)/(−1) = (2𝑦 − 1)/2 = 𝑧/4
This question is similar to Question 4 or 2nd CBSE Class 12 Sample Paper 2019 Boards

CBSE Class 12 Sample Paper for 2022 Boards (For Term 2)
CBSE Class 12 Sample Paper for 2022 Boards (For Term 2)
Last updated at Dec. 14, 2024 by Teachoo
This question is similar to Question 4 or 2nd CBSE Class 12 Sample Paper 2019 Boards
Transcript
Question 4 Find the direction cosines of the following line: (3 − 𝑥)/(−1) = (2𝑦 − 1)/2 = 𝑧/4 Given line (𝟑 − 𝒙)/(−𝟏) = (2𝑦 − 1)/2 = 𝑧/4 (−(𝑥 − 3) )/(−1) = (2𝑦 − 1)/2 = 𝑧/4 ((𝒙 − 𝟑) )/𝟏 = (2𝑦 − 1)/2 = 𝑧/4 ((𝑥 − 3) )/1 = 𝟐(𝒚 − ½)/𝟐 = 𝑧/4 ((𝑥 − 3) )/1 = ((𝒚 − ½))/𝟏 = 𝑧/4 So, direction ratios are 1, 1, 4 ½ 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 × 9) ,1/√(2 × 9) ,4/√(2 × 9) = 𝟏/(𝟑√𝟐) , 𝟏/(𝟑√𝟐) , 𝟒/(𝟑√𝟐) ½ marks