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  1. Chapter 10 Class 12 Vector Algebra (Term 2)
  2. Serial order wise

Transcript

Supplementary Exercise Q8 Find the value of ๐œ† if the point A (โˆ’1, 4, โˆ’3), B = (3, ๐œ†, โˆ’5), C(โˆ’3, 8, โˆ’5) and D (โˆ’3, 2, 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 (โˆ’1, 4, โˆ’3), B (3, ๐œ†, โˆ’5) (๐‘จ๐‘ฉ) โƒ— = (3 โ€“ (-1))๐‘– ฬ‚ + (๐œ† โˆ’ 4)๐‘— ฬ‚ + (โ€“5 โ€“(-3)) ๐‘˜ ฬ‚ = 4๐’Š ฬ‚ + (๐œ† โˆ’ 4)๐’‹ ฬ‚ โˆ’ 2๐’Œ ฬ‚ A (โˆ’1, 4, โˆ’3), C(โˆ’3, 8, โˆ’5) (๐‘จ๐‘ช) โƒ— = (-3 โ€“ (-1))๐‘– ฬ‚ + (8 โˆ’ 4)๐‘— ฬ‚ + (โ€“5 โ€“(-3)) ๐‘˜ ฬ‚ = โ€“2๐’Š ฬ‚ + 4๐’‹ ฬ‚ โˆ’ 2๐’Œ ฬ‚ A (โˆ’1, 4, โˆ’3), D (โˆ’3, 2, 1) (๐‘จ๐‘ซ) โƒ— = (-3 โ€“ (-1))๐‘– ฬ‚ + (2 โˆ’ 4)๐‘— ฬ‚ + (1 โ€“(-3)) ๐‘˜ ฬ‚ = โ€“2๐’Š ฬ‚ โ€“ 2๐’‹ ฬ‚ + 4๐’Œ ฬ‚ [(๐ด๐ต) โƒ—, (๐ด๐ถ) โƒ—, (๐ด๐ท) โƒ— ] = |โ– 8(4&(๐œ†โˆ’4)&โˆ’2@โˆ’2&4&โˆ’2@โˆ’2&โˆ’2&4)| 0 = 4[(4ร—4)โˆ’(โˆ’2ร—โˆ’2) ] โˆ’ (๐œ† โˆ’ 4) [(โˆ’2ร—4)โˆ’(โˆ’2ร—โˆ’2)] + (โˆ’2)[(โˆ’2ร—โˆ’2)โˆ’(โˆ’2ร—4) ] 0 = 4 [16โˆ’4]โˆ’"(๐œ† โˆ’ 4)" [โˆ’8โˆ’4]โˆ’2[4+8] 0 = 4(12) โ€“ "(๐œ† โˆ’ 4)"(โ€“12) โˆ’ 2 (12) 0 = 48 + 12"๐œ†" โ€“ 48 โˆ’ 24 12"๐œ†" = 24 "๐œ†" = 24/12 "๐œ†" = 2

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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.