Last updated at April 22, 2021 by Teachoo

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Ex 10.3, 16 (Introduction) Show that the points A (1, 2, 7), B (2, 6, 3) & 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 | (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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About the Author

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.