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

Transcript

Example 21 (Introduction) Show that the points A(โˆ’2๐‘– ฬ‚ + 3๐‘— ฬ‚ + 5๐‘˜ ฬ‚), B(๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚) and C(7๐‘– ฬ‚ โˆ’ ๐‘˜ ฬ‚) are collinear. (1) Three points collinear i.e. AB + BC = AC (2) Three position vectors collinear i.e. |(๐ด๐ต) โƒ— | + |(๐ต๐ถ) โƒ— | = |(๐ด๐ถ) โƒ— | Example 21 Show that the points A(โˆ’2๐‘– ฬ‚ + 3๐‘— ฬ‚ + 5๐‘˜ ฬ‚), B(๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚) and C(7๐‘– ฬ‚ โˆ’ ๐‘˜ ฬ‚) are collinear. Given A (โˆ’2๐‘– ฬ‚ + 3๐‘— ฬ‚ + 5๐‘˜ ฬ‚) B (1๐‘– ฬ‚ + 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚) C (7๐‘– ฬ‚ + 0๐‘— ฬ‚ โˆ’ 1๐‘˜ ฬ‚) 3 points A, B, C are collinear if |(๐‘จ๐‘ฉ) โƒ— | + |(๐‘ฉ๐‘ช) โƒ— | = |(๐‘จ๐‘ช) โƒ— | Finding (๐‘จ๐‘ฉ) โƒ— , (๐‘ฉ๐‘ช) โƒ— , (๐‘จ๐‘ช) โƒ— (๐‘จ๐‘ฉ) โƒ— = (1 โ€“ (-2)) ๐‘– ฬ‚ + (2 โˆ’ 3) ๐‘— ฬ‚ + (3 โˆ’ 5) ๐‘˜ ฬ‚ = 3๐’Š ฬ‚ โ€“ 1๐’‹ ฬ‚ โ€“ 2๐’Œ ฬ‚ (๐‘ฉ๐‘ช) โƒ— = (7 โˆ’ 1) ๐‘– ฬ‚ + (0 โˆ’ 2) ๐‘— ฬ‚ + (-1โˆ’3) ๐‘˜ ฬ‚ = 6๐’Š ฬ‚ โ€“ 2๐’‹ ฬ‚ โ€“ 4๐’Œ ฬ‚ (๐‘จ๐‘ช) โƒ— = (7 โˆ’ (-2)) ๐‘– ฬ‚ + (0 โˆ’ 3) ๐‘— ฬ‚ + (-1 โˆ’ 5) ๐‘˜ ฬ‚ = 9๐’Š ฬ‚ โ€“ 3๐’‹ ฬ‚ โ€“ 6๐’Œ ฬ‚ Magnitude of |(๐ด๐ต) โƒ— | = โˆš(3^2+(โˆ’1)^2+(โˆ’2)^2 ) |(๐‘จ๐‘ฉ) โƒ— | = โˆš(9+1+4) = โˆš๐Ÿ๐Ÿ’ Magnitude of |(๐ต๐ถ) โƒ— | = โˆš(6^2+(โˆ’2)^2+(โˆ’4)^2 ) |(๐‘ฉ๐‘ช) โƒ— | = โˆš(36+4+16) = โˆš56 = โˆš(4 ร— 14) = 2โˆš๐Ÿ๐Ÿ’ Magnitude of |(๐ด๐ถ) โƒ— | = โˆš(9^2+(โˆ’3)^2+(โˆ’6)^2 ) |(๐‘จ๐‘ช) โƒ— | = โˆš(81+9+36) = โˆš126 = โˆš(9 ร— 14) = 3โˆš๐Ÿ๐Ÿ’ Thus, |(๐‘จ๐‘ฉ) โƒ— | + |(๐‘ฉ๐‘ช) โƒ— | = โˆš14 + 2โˆš14 = 3โˆš14 = |(๐‘จ๐‘ช) 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 10 years. He provides courses for Maths and Science at Teachoo.