Find the unit vector in the direction of vector PQ, where P and Q are

Ex 10.2, 8 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Ex 10.2, 8 Find the unit vector in the direction of vector (๐‘ƒ๐‘„) โƒ— , where P and Q are the points (1, 2, 3) and (4, 5, 6); respectively.P (1, 2, 3) Q (4, 5, 6) (๐‘ƒ๐‘„) โƒ— = (4 โ€“ 1) ๐‘– ฬ‚ + (5 โ€“ 2) ๐‘— ฬ‚ + (6 โ€“ 3) ๐‘˜ ฬ‚ = 3๐‘– ฬ‚ + 3๐‘— ฬ‚ + 3๐‘˜ ฬ‚ โˆด Vector joining P and Q is given by (๐‘ƒ๐‘„) โƒ— = 3๐‘– ฬ‚ + 3๐‘— ฬ‚ + 3๐‘˜ ฬ‚ Magnitude of (๐‘ƒ๐‘„) โƒ— = โˆš(32+32+32) |(๐‘ƒ๐‘„) โƒ— | = โˆš(9+9+9) = โˆš27 = 3โˆš3 Unit vector in direction of (๐‘ƒ๐‘„) โƒ— = 1/(๐‘š๐‘Ž๐‘”๐‘›๐‘–๐‘ก๐‘ข๐‘‘๐‘’ ๐‘œ๐‘“ (๐‘ƒ๐‘„) โƒ— ) ร—(๐‘ƒ๐‘„) โƒ— = 1/(3โˆš3) ["3" i ฬ‚" + 3" j ฬ‚" + 3" k ฬ‚ ] = 3/(3โˆš3) ๐‘– ฬ‚ + 3/(3โˆš3) ๐‘— ฬ‚ + 3/(3โˆš3) ๐‘˜ ฬ‚ = ๐Ÿ/โˆš๐Ÿ‘ ๐’Š ฬ‚ + ๐Ÿ/โˆš๐Ÿ‘ ๐’‹ ฬ‚ + ๐Ÿ/โˆš๐Ÿ‘ ๐’Œ ฬ‚ Thus, unit vector in direction of (๐‘ƒ๐‘„) โƒ— = 1/โˆš3 ๐‘– ฬ‚ + 1/โˆš3 ๐‘— ฬ‚ + 1/โˆš3 ๐‘˜ ฬ‚

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.