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.
CBSE Class 12 Sample Paper for 2019 Boards
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CBSE Class 12 Sample Paper for 2019 Boards
Last updated at April 16, 2024 by Teachoo
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.
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