

Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at Feb. 1, 2020 by Teachoo
Transcript
Ex 11.2, 16 Find the shortest distance between the lines whose vector equations are ๐ โ = (๐ ฬ + 2๐ ฬ + 3๐ ฬ) + ๐ (๐ ฬ โ 3๐ ฬ + 2๐ ฬ) and ๐ โ = (4๐ ฬ + 5๐ ฬ + 6๐ ฬ) + ๐ (2๐ ฬ + 3๐ ฬ + ๐ ฬ)Shortest distance between the lines with vector equations ๐ โ = (๐_1 ) โ + ๐ (๐"1" ) โ and ๐ โ = (๐"2" ) โ + ๐(๐"2" ) โ is |(((๐๐) โ ร (๐๐) โ ).((๐๐) โ โ (๐๐) โ ))/|(๐๐) โ ร (๐๐) โ | | Given, ๐ โ = (๐ ฬ + 2๐ ฬ + 3๐ ฬ) + ๐ (๐ ฬ โ 3๐ ฬ + 2๐ ฬ) Comparing with ๐ โ = (๐1) โ + ๐ (๐1) โ, (๐1) โ = 1๐ ฬ + 2๐ ฬ + 3๐ ฬ & (๐1) โ = 1๐ ฬ โ 3๐ ฬ + 2๐ ฬ ๐ โ = (4๐ ฬ + 5๐ ฬ + 6๐ ฬ) + ๐(2๐ ฬ + 3๐ ฬ + ๐ ฬ) Comparing with ๐ โ = (๐2) โ + ๐(๐2) โ, (๐2) โ = 4๐ ฬ + 5๐ ฬ + 6๐ ฬ & (๐2) โ = 2๐ ฬ + 3๐ ฬ + 1๐ ฬ Now, ((๐๐) โ โ (๐๐) โ) = (4๐ ฬ + 5๐ ฬ + 6๐ ฬ) โ (1๐ ฬ + 2๐ ฬ + 3๐ ฬ) = (4 โ 1)๐ ฬ + (5 โ 2) ๐ ฬ + (6 โ 3) ๐ = 3๐ ฬ + 3๐ ฬ + 3๐ ฬ ((๐๐) โ ร (๐๐) โ) = |โ 8(๐ ฬ&๐ ฬ&๐ ฬ@1& โ3&2@2&3&1)| = ๐ ฬ [(โ3ร1)โ(3ร2)] โ ๐ ฬ [(1ร1)โ(2ร2)] + ๐ ฬ [(1ร3)โ(2รโ3)] = ๐ ฬ [โ3โ6] โ ๐ ฬ [1โ4] + ๐ ฬ [3+6] = ๐ ฬ (โ9) โ ๐ ฬ (โ3) + ๐ ฬ(9) = โ 9๐ ฬ + 3๐ ฬ + 9๐ ฬ Magnitude of ((๐1) โ ร (๐2) โ) = โ((โ 9)2+32+92) |(๐๐) โ" ร " (๐๐) โ | = โ(81+9+81) = โ171 = โ(9ร19 ) = 3โ๐๐ Also, ((๐๐) โ ร (๐๐) โ) . ((๐๐) โ โ (๐๐) โ) = (โ9๐ ฬ + 3๐ ฬ + 9๐ ฬ).(3๐ ฬ + 3๐ ฬ + 3๐ ฬ) = (โ9 ร 3) + (3 ร 3) + (9 ร 3) = โ27 + 9 + 27 = 9 So, shortest distance = |("(" (๐1) โร" " (๐2) โ")" ."(" (๐2) โ โ" " (๐1) โ")" )/|(๐1) โร (๐2) โ | | = |9/(3โ19)| = ๐/โ๐๐ Therefore, shortest distance between the given two lines is 3/โ19.
Ex 11.2
Ex 11.2, 2
Ex 11.2, 3 Important
Ex 11.2, 4
Ex 11.2, 5 Important
Ex 11.2, 6
Ex 11.2, 7 Important
Ex 11.2, 8
Ex 11.2, 9 Important
Ex 11.2, 10 Important Not in Syllabus - CBSE Exams 2021
Ex 11.2, 11 Important Not in Syllabus - CBSE Exams 2021
Ex 11.2, 12 Important
Ex 11.2, 13
Ex 11.2, 14 Important
Ex 11.2, 15 Important
Ex 11.2, 16 Important You are here
Ex 11.2, 17 Important
About the Author