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

Transcript

Ex 10.4, 9 Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5). A (1, 1, 2) , B (2, 3, 5) , C (1, 5, 5) Area of triangle ABC is 1/2 |(๐ด๐ต) โƒ— ร— (๐ด๐ถ) โƒ— | A (1, 1, 2) B (2, 3, 5) (๐ด๐ต) โƒ— = (2 โˆ’ 1) ๐‘– ฬ‚ + (3 โˆ’ 1) ๐‘— ฬ‚ + (5 โˆ’ 2) ๐‘˜ ฬ‚ = 1๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚ A (1, 1, 2) C (1, 5, 5) (๐ด๐ถ) โƒ— = (1 โˆ’ 1) ๐‘– ฬ‚ + (5 โˆ’ 1) ๐‘— ฬ‚ + (5 โˆ’ 2) ๐‘˜ ฬ‚ = 0๐‘– ฬ‚ + 4๐‘— ฬ‚ + 3๐‘˜ ฬ‚ (๐‘จ๐‘ฉ) โƒ— ร— (๐‘จ๐‘ช) โƒ— = |โ– 8(๐‘– ฬ‚&๐‘— ฬ‚&๐‘˜ ฬ‚@1&2&3@0&4&3)| = ๐‘– ฬ‚ (2ร—3โˆ’4ร—3 )โˆ’๐‘— ฬ‚ (1ร—3โˆ’0ร—3 )+๐‘˜ ฬ‚ (1ร—4โˆ’0ร—2 ) = ๐‘– ฬ‚ (6โˆ’12)โˆ’๐‘— ฬ‚(3โˆ’0) + ๐‘˜ ฬ‚ (4โˆ’0) = โˆ’6๐’Š ฬ‚ โ€“ 3๐’‹ ฬ‚ + 4๐’Œ ฬ‚ Magnitude of (๐ด๐ต) โƒ— ร— (๐ด๐ถ) โƒ— = โˆš((โˆ’6)2+(โˆ’3)2+42) |(๐ด๐ต) โƒ—" ร— " (๐ด๐ถ) โƒ— | = โˆš(36+9+16) = โˆš61 Area of triangle ABC = 1/2 |(๐ด๐ต) โƒ—" ร— " (๐ด๐ถ) โƒ— | = 1/2 ร— โˆš61 = โˆš๐Ÿ”๐Ÿ/๐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 9 years. He provides courses for Maths and Science at Teachoo.