

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
Example 11 You are here
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 Feb. 1, 2020 by Teachoo
Example 11 Find the shortest distance between the lines l1 and l2 whose vector equations are π β = π Μ + π Μ + π(2π Μ β π Μ + π Μ ) and π β = 2π Μ + π Μ β π Μ + π (3π Μ β 5π Μ + 2π Μ )Shortest distance between lines with vector equations π β = (π1) β + π (π1) β and π β = (π2) β + π(π2) β is |(((π1) β Γ (π2) β ).((π2) β β (π1) β ))/|(π1) β Γ (π2) β | | π β = (π Μ + π Μ) + π (2π Μ β π Μ + π Μ) Comparing with π β = (π1) β + π (π1) β (π1) β = 1π Μ + 1π Μ + 0π Μ & (π1) β = 2π Μ β 1π Μ + 1π Μ π β = (2π Μ + π Μ β π Μ) + π (3π Μ β 5π Μ + 2π Μ) Comparing with π β = (π2) β + π(π2) β (π2) β = 2π Μ + 1π Μ β 1π Μ & (π2) β = 3π Μ β 5π Μ + 2π Μ Now (ππ) β β (ππ) β = (2π Μ + 1π Μ β 1π Μ) β (1π Μ + 1π Μ + 0π Μ) = (2 β 1) π Μ + (1 β 1)π Μ + (β1 β 0) π Μ = 1π Μ + 0π Μ β 1π Μ (ππ) β Γ (ππ) β = |β 8(π Μ&π Μ&π Μ@2& β1&1@3& β5&2)| = π Μ [(β1Γ2)β(β5Γ1)] β π Μ [(2Γ2)β(3Γ1)] + π Μ[(2Γβ5)β(3Γβ1)] = π Μ [β2+5] β π Μ [4β3] + π Μ [β10+3] = π Μ (3) β π Μ (1) + π Μ(β7) = 3π Μ β π Μ β 7π Μ Magnitude of ((π1) β Γ (π2) β) = β(32+(β1)2+(β7)^2 ) |(ππ) βΓ (ππ) β | = β(9+1+49) = βππ Also, ((ππ) β Γ (ππ) β) .((ππ) β β (ππ) β) = (3π Μ β π Μ β 7π Μ) . (1π Μ + 0π Μ β 1π Μ) = (3 Γ 1) + (β1 Γ 0) + (β7 Γ β1) = 3 + 0 + 7 = 10 β΄ Shortest distance = |(((π1) β Γ (π2) β ).((π2) β β (π1) β ))/|(π1) β Γ (π2) β | | = |10/β59| = ππ/βππ .