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Last updated at Feb. 1, 2020 by Teachoo
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Ex 10.5, 6 (Supplementary NCERT) Find x such that A (3, 2, 1), B = (4, x, 5), C(4, 2, โ2) and D (6, 5, โ1) are coplanar Four points A, B, C, D are coplanar if the three vectors (๐ด๐ต) โ , (๐ด๐ถ) โ and (๐ด๐ท) โ are coplanar. i.e. [(๐จ๐ฉ) โ, (๐จ๐ช) โ, (๐จ๐ซ) โ ] = 0 A (3, 2, 1), B (4, x, 5) (๐จ๐ฉ) โ = (4 โ 3)๐ ฬ + (x โ 2)๐ ฬ + (5 โ 1) ๐ ฬ = 1๐ ฬ + (x โ 2)๐ ฬ + 4๐ ฬ A (3, 2, 1), C(4, 2, โ2) (๐จ๐ช) โ = (4 โ 3)๐ ฬ + (2 โ 2)๐ ฬ + (โ2 โ 1) ๐ ฬ = 1๐ ฬ + 0๐ ฬ โ 3๐ ฬ A (3, 2, 1), D (6, 5, โ1) (๐จ๐ซ) โ = (6 โ 3)๐ ฬ + (5 โ 2)๐ ฬ + (โ1 โ 1) ๐ ฬ = 3๐ ฬ + 3๐ ฬ โ 2๐ ฬ [(๐ด๐ต) โ, (๐ด๐ถ) โ, (๐ด๐ท) โ ] = |โ 8(1&(๐ฅโ2)&4@1&0&โ3@3&3&โ2)| 0 = 1[(0รโ2)โ(3รโ3) ] โ (x โ 2) [(1รโ2)โ(3รโ3)] + 4[(1ร3)โ(3ร0) ] 0 = 1[0โ(โ9)]โ"(x โ 2)" [โ2โ(โ9)]+4[3โ0] 0 = 1(9) โ "(x โ 2)"(โ2 + 9) + 4(3) 0 = 9 โ (x โ 2) (7) + 12 0 = 9 โ 7x + 14 + 12 0 = 35 โ 7x 7x = 35 x = 35/7 x = 5
Ex 10.5 (Supplementary NCERT)
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