Ex 11.2

Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

Β

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### Transcript

Angle between the pair of lines (π₯ β π₯1)/π1 = (π¦ β π¦1)/π1 = (π§ β π§1)/π1 and (π₯ β π₯2)/π2 = (π¦ β π¦2)/π2 = (π§ β π§2)/π2 is given by cos ΞΈ = |(π_π π_π + π_π π_π +γ πγ_π π_π)/(β(γπ_πγ^π + γπ_πγ^π+ γπ_πγ^π ) β(γπ_πγ^π +γγ πγ_πγ^π+ γπ_πγ^π ))| π/π = π/π = π/π (π₯ β 0)/2 = (π¦ β 0)/2 = (π§ β 0)/1 Comparing with (π₯ β π₯1)/π1 = (π¦ β π¦1)/π1 = (π§ β π§1)/π1 x1 = 0, y1 = 0, z1 = 0 & π1 = 2, b1 = 2, c1 = 1 (π β π)/π = (π β π)/π = (π β π)/π Comparing with (π₯ β π₯2)/π2 = (π¦ β π¦2)/π2 = (π§ β π§2)/π2 π₯2 = 5, y2 = 2, z2 = 5 & π2 = 4, π2 = 1, π2 = 8 Now, cos ΞΈ = |(π_π π_π + π_π π_π +γ πγ_π π_π)/(β(γπ_πγ^π + γπ_πγ^π+ γπ_πγ^π ) β(γπ_πγ^π +γγ πγ_πγ^π+ γπ_πγ^π ))| = |((2 Γ 4) + (2 Γ 1) + (1 Γ 8) )/(β(22 + 22 + 12) Γ β(42 + 12 + 82))| = |(8 + 2 + 8 )/(β(4 + 4 + 1) β(16 + 1 + 64))| = |18/(β9 Γ β81)| = 18/(3 Γ 9) = 2/3 So, cos ΞΈ = 2/3 β΄ ΞΈ = cos-1 (π/π) Therefore, the angle between the given lines is cosβ1(π/π).