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

Transcript

Ex 10.3, 16 (Introduction) Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, โ€“1) are collinear. (1) Three points collinear i.e. AB + BC = AC (2) Three vectors collinear i.e. |(๐ด๐ต) โƒ— | + |(๐ต๐ถ) โƒ— | = |(๐ด๐ถ) โƒ— | Ex 10.3, 16 Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, โ€“1) are collinear. 3 points A, B, C are collinear if i.e. |(๐‘จ๐‘ฉ) โƒ— | + |(๐‘ฉ๐‘ช) โƒ— | = |(๐‘จ๐‘ช) โƒ— | A (1, 2, 7) B (2, 6, 3) C (3, 10, โ€“1) (๐ด๐ต) โƒ— = (2 โˆ’ 1) ๐‘– ฬ‚ + (6 โˆ’ 2) ๐‘— ฬ‚ + (3 โˆ’ 7) ๐‘˜ ฬ‚ = 1๐‘– ฬ‚ + 4๐‘— ฬ‚ โˆ’ 4๐‘˜ ฬ‚ (๐ต๐ถ) โƒ— = (3 โˆ’ 2) ๐‘– ฬ‚ + (10 โˆ’ 6) ๐‘— ฬ‚ + (โˆ’1 โˆ’ 3) ๐‘˜ ฬ‚ = 1๐‘– ฬ‚ + 4๐‘— ฬ‚ โˆ’ 4๐‘˜ ฬ‚ (๐ด๐ถ) โƒ— = (3 โˆ’ 1) ๐‘– ฬ‚ + (10 โˆ’ 2) ๐‘— ฬ‚ + (โˆ’1 โˆ’ 7) ๐‘˜ ฬ‚ = 2๐‘– ฬ‚ + 8๐‘— ฬ‚ โˆ’ 8๐‘˜ ฬ‚ Magnitude of (๐ด๐ต) โƒ— = โˆš(12+42+(โˆ’4)2) |(๐ด๐ต) โƒ— | = โˆš(1+16+16) = โˆš33 Magnitude of (๐ต๐ถ) โƒ— = โˆš(12+42+(โˆ’4)2) |(๐ต๐ถ) โƒ— | = โˆš(1+16+16) = โˆš33 Magnitude of (๐ด๐ถ) โƒ— = โˆš(22+82+(โˆ’8)2) |(๐ต๐ถ) โƒ— | = โˆš(4+64+64) = โˆš132 = โˆš(4ร—33 )= 2โˆš(33 ) Thus, |(๐ด๐ต) โƒ— | + |(๐ต๐ถ) โƒ— | = โˆš(33 ) + โˆš(33 ) = 2โˆš(33 ) = |(๐ด๐ถ) โƒ— | Thus, A, B and C are collinear.

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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.