Slide38.JPG

Slide39.JPG
Slide40.JPG

Subscribe to our Youtube Channel - https://you.tube/teachoo

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise

Transcript

Misc 13 The scalar product of the vector ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ with a unit vector along the sum of vectors 2๐‘– ฬ‚ + 4๐‘— ฬ‚ โˆ’ 5๐‘˜ ฬ‚ and ฮป๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚ is equal to one. Find the value of ฮป. Let ๐‘Ž โƒ— = ๐‘– ฬ‚ + ๐‘— ฬ‚ + ๐‘˜ ฬ‚ = 1๐‘– ฬ‚ + 1๐‘— ฬ‚ + 1๐‘˜ ฬ‚ ๐‘ โƒ— = 2๐‘– ฬ‚ + 4๐‘— ฬ‚ โ€“ 5๐‘˜ ฬ‚ ๐‘ โƒ— = ๐œ† ๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚ (๐‘ โƒ— + ๐‘ โƒ—) = (2 + ๐œ†) ๐‘– ฬ‚ + (4 + 2) ๐‘— ฬ‚ + (โˆ’5 + 3) ๐‘˜ ฬ‚ = (2 + ๐œ†) ๐‘– ฬ‚ + 6๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚ Let ๐‘Ÿ ฬ‚ be unit vector along (๐‘ โƒ— + ๐‘ โƒ—) ๐‘Ÿ ฬ‚ = 1/(๐‘€๐‘Ž๐‘”๐‘›๐‘–๐‘ก๐‘ข๐‘‘๐‘’ ๐‘œ๐‘“ (๐‘ โƒ—" + " ๐‘ โƒ—)) ร— (๐‘ โƒ— + ๐‘ โƒ—) ๐‘Ÿ ฬ‚ = 1/โˆš((2 + ๐œ†)^2 + 6^2 + (โˆ’2)^2 ) ร— ((2 + ๐œ†) ๐‘– ฬ‚ + 6๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚) ๐‘Ÿ ฬ‚ = 1/โˆš(2^2 + ๐œ†^2 + 4๐œ† + 36 + 4) ร— ((2 + ๐œ†) ๐‘– ฬ‚ + 6๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚) ๐’“ ฬ‚ = ๐Ÿ/โˆš(๐€^๐Ÿ + ๐Ÿ’๐€ +๐Ÿ’๐Ÿ’) ร— ((2 + ๐œ†) ๐’Š ฬ‚ + 6๐’‹ ฬ‚ โˆ’ 2๐’Œ ฬ‚) Given, ๐‘Ž โƒ—. (๐‘Ÿ ฬ‚) = 1 (1๐‘– ฬ‚ + 1๐‘— ฬ‚ + 1๐‘˜ ฬ‚). (1/โˆš(๐œ†^2 + 4๐œ† +44) " ร— ((2 + ๐œ†) " ๐‘– ฬ‚" + 6" ๐‘— ฬ‚" โˆ’ 2" ๐‘˜ ฬ‚")" ) = 1 1/โˆš(๐œ†^2 + 4๐œ† +44) (1๐‘– ฬ‚ + 1๐‘— ฬ‚ + 1๐‘˜ ฬ‚).((๐œ† +2) ๐‘– ฬ‚ + 6๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚) = 1 (1๐‘– ฬ‚ + 1๐‘— ฬ‚ + 1๐‘˜ ฬ‚).((๐œ† +2) ๐‘– ฬ‚ + 6๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚) = โˆš(๐œ†^2 + 4๐œ† +44) 1.(๐œ† + 2) + 1.6 + 1.(โˆ’2) = โˆš(๐œ†^2 + 4๐œ† +44) ๐œ† + 2 + 6 โˆ’ 2 = โˆš(๐œ†^2 + 4๐œ† +44) ๐œ† + 6 = โˆš(๐€^๐Ÿ + ๐Ÿ’๐€ +๐Ÿ’๐Ÿ’) Squaring both sides (๐œ† + 6)2 = (โˆš(๐œ†^2 + 4๐œ† +44))^2 ๐œ†2 + 36 + 12๐œ† = ๐œ†^2 + 4๐œ† +44 ๐œ†2 โ€“ ๐œ†^2 + 12๐œ† โ€“ 4๐œ† = 44 โ€“ 36 8๐œ† = 8 ๐œ† = 8/8 ๐œ† = 1 So, ๐œ† = 1

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.