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.

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Question 4 (OR 1st question) Find the acute angle which the line with direction cosines 1/โˆš3, 1/โˆš6 , n makes with positive direction of z-axis. Given ๐‘™ = 1/โˆš3 ๐‘š = 1/โˆš6 ๐‘› = ? We need to find n We know that ๐‘™^2+๐‘š^2+๐‘›^2=1 (1/โˆš3)^2+(1/6)^2+๐‘›^2=1 1/3+1/6+ ๐‘›^2=1 (2 + 1)/6+ ๐‘›^2=1 3/6+ ๐‘›^2=1 1/2+ ๐‘›^2=1 ๐‘›^2=1 โ€“ 1/2 ๐‘›^2=1/2 n=ยฑโˆš(1/2) n=ยฑ1/โˆš2 Since we need the angle with positive direction of x-axis, We take positive value of n n = 1/โˆš2 We know that cos ๐›พ = n cos ๐›พ = 1/โˆš2 So, ๐›พ = 45ยฐ ๐›พ = ๐œ‹/4 So,, line makes ๐œ‹/4 angle with the positive direction of z0axis Since we need the angle with positive direction of x-axis, We take positive value of n n = 1/โˆš2 We know that cos ๐›พ = n cos ๐›พ = 1/โˆš2 So, ๐›พ = 45ยฐ ๐œธ = ๐…/๐Ÿ’ So, line makes ๐œ‹/4 angle with the positive direction of z-axis

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.