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Last updated at Jan. 31, 2020 by Teachoo
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Example 21 (Introduction) Show that the points A(โ2๐ ฬ + 3๐ ฬ + 5๐ ฬ), B(๐ ฬ + 2๐ ฬ + 3๐ ฬ) and C(7๐ ฬ โ ๐ ฬ) are collinear. (1) Three points collinear i.e. AB + BC = AC (2) Three vectors collinear i.e. |(๐ด๐ต) โ | + |(๐ต๐ถ) โ | = |(๐ด๐ถ) โ | Example 21 Show that the points A(โ2๐ ฬ + 3๐ ฬ + 5๐ ฬ), B(๐ ฬ + 2๐ ฬ + 3๐ ฬ) and C(7๐ ฬ โ ๐ ฬ) are collinear. 3 points A, B, C are collinear if |(๐จ๐ฉ) โ | + |(๐ฉ๐ช) โ | = |(๐จ๐ช) โ | A (โ2๐ ฬ + 3๐ ฬ + 5๐ ฬ) B (1๐ ฬ + 2๐ ฬ + 3๐ ฬ) C (7๐ ฬ + 0๐ ฬ โ 1๐ ฬ) (๐ด๐ต) โ = (1 โ (-2)) ๐ ฬ + (2 โ 3) ๐ ฬ + (3 โ 5) ๐ ฬ = 3๐ ฬ โ 1๐ ฬ โ 2๐ ฬ (๐ต๐ถ) โ = (7 โ 1) ๐ ฬ + (0 โ 2) ๐ ฬ + (-1โ3) ๐ ฬ = 6๐ ฬ โ 2๐ ฬ โ 4๐ ฬ (๐ด๐ถ) โ = (7 โ (-2)) ๐ ฬ + (0 โ 3) ๐ ฬ + (-1 โ 5) ๐ ฬ = 9๐ ฬ โ 3๐ ฬ โ 6๐ ฬ Magnitude of |(๐ด๐ต) โ | = โ(3^2+(โ1)^2+(โ2)^2 ) |(๐ด๐ต) โ | = โ(9+1+4) = โ๐๐ Magnitude of |(๐ต๐ถ) โ | = โ(6^2+(โ2)^2+(โ4)^2 ) |(๐ต๐ถ) โ | = โ(36+4+16) = โ56 = โ(4ร14) = 2โ๐๐ Magnitude of |(๐ด๐ถ) โ | = โ(9^2+(โ3)^2+(โ6)^2 ) |(๐ด๐ถ) โ | = โ(81+9+36) = โ126 = โ(9ร14) = 3โ๐๐ Thus, |(๐ด๐ต) โ | + |(๐ต๐ถ) โ | = โ14 + 2โ14 = 3โ14 = |(๐ด๐ถ) โ | Thus, A, B and C are collinear.
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Example 26 (Supplementary NCERT) Not in Syllabus - CBSE Exams 2021
Example 27 (Supplementary NCERT) Not in Syllabus - CBSE Exams 2021
Example 28 (Supplementary NCERT) Important Not in Syllabus - CBSE Exams 2021
Example 29 (Supplementary NCERT) Important Not in Syllabus - CBSE Exams 2021
Example 30 (Supplementary NCERT) Important Not in Syllabus - CBSE Exams 2021
Example 31 (Supplementary NCERT) Important Not in Syllabus - CBSE Exams 2021
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