Ex 11.2

Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

Β

Β

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### 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 ))| 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 β π)/π = (π β π)/π = (π + π)/( β π) (π₯ β 2)/2 = (π¦ β 1)/5 = (π§ β (β3))/( β 3) Comparing with (π₯ β π₯1)/π1 = (π¦ β π¦1)/π1 = (π§ β π§1)/π1 x1 = 2, y1 = 1, z1 = β3 & π1 = 2, b1 = 5, c1 = β3 (π + π)/( β π) = (π β π)/π = (π β π)/π (π₯ β (β 2))/( β 1) = (π¦ β 4)/8 = (π§ β 5)/4 Comparing with (π₯ β π₯2)/π2 = (π¦ β π¦2)/π2 = (π§ β π§2)/π2 π₯2 = β 2, y2 = 4, z2 = 5 & π2 = β1, π2 = 8, π2 = 4 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 β1) + (5 Γ 8) + ( β 3 Γ 4) )/(β(2^2 + 5^2 + γ(β3)γ^2 ) β(γ(β1)γ^2 + 8^2 + 4^2 ))| = |( β2 + 40 + (β12) )/(β(4 + 25 + 9) β(1 + 64 + 16))| = |26/(β38 β81)| = |26/(β38 Γ 9)| = 26/(9β38 ) So, cos ΞΈ = 26/(9β38 ) β΄ ΞΈ = cosβ1 (ππ/(πβππ )) Therefore, the angle between the given lines is cos-1 (26/(9β38 )). = |( β2 + 40 + (β12) )/(β(4 + 25 + 9) β(1 + 64 + 16))| = |26/(β38 β81)| = |26/(β38 Γ 9)| = 26/(9β38 ) So, cos ΞΈ = 26/(9β38 ) β΄ ΞΈ = cosβ1 (ππ/(πβππ )) Therefore, the angle between the given lines is cos-1 (26/(9β38 )).