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Last updated at Jan. 31, 2020 by Teachoo
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Ex 10.3, 16 (Introduction) Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, โ1) are collinear. (1) Three points collinear i.e. AB + BC = AC (2) Three vectors collinear i.e. |(๐ด๐ต) โ | + |(๐ต๐ถ) โ | = |(๐ด๐ถ) โ | Ex 10.3, 16 Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, โ1) are collinear. 3 points A, B, C are collinear if i.e. |(๐จ๐ฉ) โ | + |(๐ฉ๐ช) โ | = |(๐จ๐ช) โ | A (1, 2, 7) B (2, 6, 3) C (3, 10, โ1) (๐ด๐ต) โ = (2 โ 1) ๐ ฬ + (6 โ 2) ๐ ฬ + (3 โ 7) ๐ ฬ = 1๐ ฬ + 4๐ ฬ โ 4๐ ฬ (๐ต๐ถ) โ = (3 โ 2) ๐ ฬ + (10 โ 6) ๐ ฬ + (โ1 โ 3) ๐ ฬ = 1๐ ฬ + 4๐ ฬ โ 4๐ ฬ (๐ด๐ถ) โ = (3 โ 1) ๐ ฬ + (10 โ 2) ๐ ฬ + (โ1 โ 7) ๐ ฬ = 2๐ ฬ + 8๐ ฬ โ 8๐ ฬ Magnitude of (๐ด๐ต) โ = โ(12+42+(โ4)2) |(๐ด๐ต) โ | = โ(1+16+16) = โ33 Magnitude of (๐ต๐ถ) โ = โ(12+42+(โ4)2) |(๐ต๐ถ) โ | = โ(1+16+16) = โ33 Magnitude of (๐ด๐ถ) โ = โ(22+82+(โ8)2) |(๐ต๐ถ) โ | = โ(4+64+64) = โ132 = โ(4ร33 )= 2โ(33 ) Thus, |(๐ด๐ต) โ | + |(๐ต๐ถ) โ | = โ(33 ) + โ(33 ) = 2โ(33 ) = |(๐ด๐ถ) โ | Thus, A, B and C are collinear.
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