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 𝑚 = 1/√6 𝑛 = ? We need to find n We know that 𝑙^2+𝑚^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=±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 = 45° 𝜸 = 𝝅/𝟒 So, line makes 𝜋/4 angle with the positive direction of z-axis

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.