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Ex 10.5, 6 (Supplementary NCERT) - Find x such that A (3, 2, 1), B (4,

Ex 10.5, 6 (Supplementary NCERT) - Chapter 10 Class 12 Vector Algebra - Part 2

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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, โ€“2) and D (6, 5, โ€“1) are coplanar Four points A, B, C, D are coplanar if the three vectors (๐ด๐ต) โƒ— , (๐ด๐ถ) โƒ— and (๐ด๐ท) โƒ— are coplanar. i.e. [(๐‘จ๐‘ฉ) โƒ—, (๐‘จ๐‘ช) โƒ—, (๐‘จ๐‘ซ) โƒ— ] = 0 A (3, 2, 1), B (4, x, 5) (๐‘จ๐‘ฉ) โƒ— = (4 โ€“ 3)๐‘– ฬ‚ + (x โˆ’ 2)๐‘— ฬ‚ + (5 โ€“ 1) ๐‘˜ ฬ‚ = 1๐’Š ฬ‚ + (x โˆ’ 2)๐’‹ ฬ‚ + 4๐’Œ ฬ‚ A (3, 2, 1), C (4, 2, โ€“2) (๐‘จ๐‘ช) โƒ— = (4 โ€“ 3)๐‘– ฬ‚ + (2 โ€“ 2)๐‘— ฬ‚ + (โ€“2 โ€“ 1) ๐‘˜ ฬ‚ = 1๐’Š ฬ‚ + 0๐’‹ ฬ‚ โˆ’ 3๐’Œ ฬ‚ A (3, 2, 1), D (6, 5, โ€“1) (๐‘จ๐‘ซ) โƒ— = (6 โ€“ 3)๐‘– ฬ‚ + (5 โ€“ 2)๐‘— ฬ‚ + (โ€“1 โ€“ 1) ๐‘˜ ฬ‚ = 3๐’Š ฬ‚ + 3๐’‹ ฬ‚ โ€“ 2๐’Œ ฬ‚ Now, [(๐ด๐ต) โƒ—, (๐ด๐ถ) โƒ—, (๐ด๐ท) โƒ— ] = |โ– 8(1&(๐‘ฅโˆ’2)&4@1&0&โˆ’3@3&3&โˆ’2)| 0 = 1[(0ร—โˆ’2)โˆ’(3ร—โˆ’3) ] โˆ’ (x โˆ’ 2) [(1ร—โˆ’2)โˆ’(3ร—โˆ’3)] + 4[(1ร—3)โˆ’(3ร—0) ] 0 = 1[0โˆ’(โˆ’9)]โˆ’"(x โˆ’ 2)" [โˆ’2โˆ’(โˆ’9)]+4[3โˆ’0] 0 = 1(9) โ€“ "(x โˆ’ 2)"(โ€“2 + 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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.