This question is the same as Example 27 (Supplementary NCERT)

Ex 10.5, 2 (Supplementary NCERT) - Show that a = i - 2j + 3k, b = -2i

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

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

Transcript

Ex 10.5, 2 (Supplementary NCERT) Show that the vectors ๐‘Ž โƒ— = ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚, ๐‘ โƒ— = โˆ’2๐‘– ฬ‚ + 3๐‘— ฬ‚ โˆ’ 4๐‘˜ ฬ‚ and ๐‘ โƒ— = ๐‘– ฬ‚ โˆ’ 3๐‘— ฬ‚ + 5๐‘˜ ฬ‚ are coplanarThree vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar if [๐’‚ โƒ—" " ๐’ƒ โƒ—" " ๐’„ โƒ— ] = 0 Given, ๐’‚ โƒ— = ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + 3๐‘˜ ฬ‚ ๐’ƒ โƒ— = โˆ’2๐‘– ฬ‚ + 3๐‘— ฬ‚ โˆ’ 4๐‘˜ ฬ‚ ๐’„ โƒ— = ๐‘– ฬ‚ โˆ’ 3๐‘— ฬ‚ + ฮป๐‘˜ ฬ‚ Now, [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = |โ– 8(1&โˆ’2&3@โˆ’2&3&โˆ’4@1&โˆ’3&5)| = 1[(3ร—5)โˆ’(โˆ’3ร—โˆ’4) ] โˆ’ (โˆ’2) [(โˆ’2ร—5)โˆ’(1ร—โˆ’4) ] + 3[(โˆ’2ร—โˆ’3)โˆ’(1ร—3) ] = 1 [15โˆ’(3 ร—4)]+2[โˆ’10โˆ’(โˆ’4)]+3[(2 ร—3)โˆ’3] = 1 [15โˆ’12]+2[โˆ’10+4]+3[6โˆ’3] = 1 [3]+2[โˆ’6]+3[3] = 3 โ€“ 12 + 9 = 0 Since [๐‘Ž โƒ—" " ๐‘ โƒ—" " ๐‘ โƒ— ] = 0 Vectors ๐‘Ž โƒ—, ๐‘ โƒ—, ๐‘ โƒ— are coplanar

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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.