

Examples
Example, 2 Important
Example, 3
Example, 4 Important
Example, 5 Important
Example, 6 Important
Example, 7
Example 8
Example, 9 Deleted for CBSE Board 2022 Exams
Example 10 Important Deleted for CBSE Board 2022 Exams You are here
Example 11
Example 12 Important
Example 13 Important
Example 14
Example 15
Example 16 Important
Example 17
Example 18
Example 19 Important
Example 20 Important
Example 21 Important
Example 22 Deleted for CBSE Board 2022 Exams
Example 23 Important Deleted for CBSE Board 2022 Exams
Example 24
Example, 25 Important Deleted for CBSE Board 2022 Exams
Example 26
Example 27 Important
Example 28 Important
Example 29 Important
Example 30 Important
Last updated at Aug. 23, 2021 by Teachoo
Example 10 Find the angle between the pair of lines (π₯ + 3)/3 = (π¦ β 1)/5 = (π§ + 3)/4 and (π₯ + 1)/1 = (π¦ β 4)/1 = (π§ β 5)/2Angle between the pair of lines (π₯ β π₯1)/π1 = (π¦ β π¦1)/π1 = (π§ β π§1)/π1 and (π₯ β π₯2)/π2 = (π¦ β π¦2)/π2 = (π§ β π§2)/π2 is given by cos ΞΈ = |(π_π π_π + π_π π_π +γ πγ_π π_π)/(β(γπ_πγ^π + γπ_πγ^π+ γπ_πγ^π ) β(γπ_πγ^π +γγ πγ_πγ^π+ γπ_πγ^π ))| (π + π)/π = (π β π)/π = (π + π)/π (π₯ β (β3))/3 = (π¦ β 1)/5 = (π§ β (β3))/4 Comparing with (π₯ β π₯1)/π1 = (π¦ β π¦1)/π1 = (π§ β π§1)/π1 x1 = β3, y1 = 1, z1 = β3 & π1 = 3, b1 = 5, c1 = 4 (π + π)/π = (π β π)/π = (π β π)/π (π₯ β (β1))/1 = (π¦ β 4)/1 = (π§ β 5)/2 Comparing with (π₯ β π₯2)/π2 = (π¦ β π¦2)/π2 = (π§ β π§2)/π2 π₯2 = β1, y2 = 4, z2 = 5 & π2 = 1, π2 = 1, π2 = 2 Now, cos ΞΈ = |(π_1 π_2 + π_1 π_2 +γ πγ_1 π_2)/(β(γπ_1γ^2 + γπ_1γ^2+ γπ_1γ^2 ) β(γπ_2γ^2 +γγ πγ_2γ^2+ γπ_2γ^2 ))| = |((3 Γ 1) + (5 Γ 1) + (4 Γ 2))/(β(3^2 + 5^2 + 4^2 ) Γ β(1^2 + 1^2 + 2^2 ))| = |(3 + 5 + 8)/(β(9 + 25 + 16) β(1 + 1 + 4))| = |16/(β50 β6)| = |16/(5β2 Γ β2 β3)| = |16/(5 Γ 2 Γ β3)| = 8/(5 β3) = 8/(5 β3) Γ β3/β3 = (8β3)/(15 ) So, cos ΞΈ = (8β3)/(15 ) β΄ ΞΈ = cos-1((πβπ)/(ππ )) Therefore, the angle between the given pair of line is cosβ1 ((8β3)/(15 ))