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Question 4 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at March 30, 2023 by

Question 4 (OR 1 st question)

Find the acute angle which the line with direction cosines 1/√3, 1/√6, n makes with positive direction of z-axis.

Find the angle which line with direction cosines 1/√3, 1/√6, n makes

Question 4 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 2
Question 4 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 3

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Transcript

Question 4 (OR 1st question) Find the acute angle which the line with direction cosines 1/√3, 1/√6 , n makes with positive direction of z-axis. Given 𝑙 = 1/√3 π‘š = 1/√6 𝑛 = ? We need to find n We know that 𝑙^2+π‘š^2+𝑛^2=1 (1/√3)^2+(1/√6)^2+𝑛^2=1 1/3+1/6+ 𝑛^2=1 (2 + 1)/6+ 𝑛^2=1 3/6+ 𝑛^2=1 1/2+ 𝑛^2=1 𝑛^2=1 – 1/2 𝑛^2=1/2 n=±√(1/2) n=Β±1/√2 Since we need the angle with positive direction of x-axis, We take positive value of n n = 1/√2 We know that cos 𝛾 = n cos 𝛾 = 1/√2 So, 𝛾 = 45Β° 𝜸 = 𝝅/πŸ’ So, line makes πœ‹/4 angle with the positive direction of z-axis

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