Ex 10.4, 1 Class 12 - NCERT Solutions Vector Algebra - Find |a x b|

Ex 10.4, 1 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Ex 10.4, 1 Find |๐‘Ž โƒ—ร—๐‘ โƒ— |, if ๐‘Ž โƒ— = ๐‘– ฬ‚ โˆ’ 7๐‘— ฬ‚ + 7๐‘˜ ฬ‚ and ๐‘ โƒ— = 3๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + 2๐‘˜ ฬ‚๐‘Ž โƒ— = ๐‘– ฬ‚ โˆ’ 7๐‘— ฬ‚ + 7๐‘˜ ฬ‚ = 1๐‘– ฬ‚ โˆ’ 7๐‘— ฬ‚ + 7๐‘˜ ฬ‚ ๐‘ โƒ— = 3๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + 2k ฬ‚ ๐‘Ž โƒ— ร— ๐‘ โƒ— = |โ– 8(๐‘– ฬ‚&๐‘— ฬ‚&๐‘˜ ฬ‚@โ–ˆ(1@3)&โ–ˆ(โˆ’7@โˆ’2)&โ–ˆ(7@2))| = ๐‘– ฬ‚ |โ– 8(โˆ’7&7@โˆ’2&2)| โˆ’๐‘— ฬ‚ |โ– 8(1&7@3&2)| + k ฬ‚ |โ– 8(1&โˆ’7@3&โˆ’2)| = ๐‘– ฬ‚ ("โˆ’7 ร— 2 โ€“ (โˆ’2 ร— 7)" ) โˆ’ ๐‘— ฬ‚((1ร—2 ) โˆ’ (3ร—7 )) + ๐‘˜ ฬ‚((1ร—2 ) โˆ’ (3 ร— โˆ’7)) = ๐‘– ฬ‚ (โˆ’14โˆ’(โˆ’14)) โˆ’ ๐‘— ฬ‚(2โˆ’21 ) + ๐‘˜ ฬ‚((โˆ’2โˆ’(โˆ’21)) = ๐‘– ฬ‚ (0) โˆ’ ๐‘— ฬ‚ (โˆ’19) + ๐‘˜ ฬ‚(19) = 0๐‘– ฬ‚ + 19๐‘— ฬ‚ + 19๐‘˜ ฬ‚ โˆด ๐’‚ โƒ— ร— ๐’ƒ โƒ— = 0๐’Š ฬ‚ + 19๐’‹ ฬ‚ + 19๐’Œ ฬ‚ Magnitude of ๐‘Ž โƒ— ร— ๐‘ โƒ— = โˆš(02+192+192) |๐’‚ โƒ—" ร—" ๐’ƒ โƒ— | = โˆš(0+361+361) = โˆš722 = โˆš(19ร—19ร—2 ) = 19โˆš๐Ÿ Therefore, the magnitude of ๐‘Ž โƒ—" ร—" ๐‘ โƒ— is 19โˆš๐Ÿ.

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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.