Ex 10.4, 10 - Find area of parallelogram whose adjacent sides are

Ex 10.4, 10 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Ex 10.4, 10 Find the area of the parallelogram whose adjacent sides are determined by the vectors ๐‘Ž โƒ— = ๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + 3๐‘˜ ฬ‚ and b = 2๐‘– ฬ‚ โˆ’ 7๐‘— ฬ‚ + ๐‘˜ ฬ‚ . ๐‘Ž โƒ— = ๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + 3๐‘˜ ฬ‚ = 1๐‘– ฬ‚ โˆ’ 1๐‘— ฬ‚ + 3k ฬ‚ ๐‘ โƒ— = 2๐‘– ฬ‚ โˆ’ 7๐‘— ฬ‚ + ๐‘˜ ฬ‚ = 2๐‘– ฬ‚ โˆ’ 7๐‘— ฬ‚ + 1k ฬ‚ Area of parallelogram ABCD = |๐‘Ž โƒ—" ร— " ๐‘ โƒ— | ๐’‚ โƒ— ร— ๐’ƒ โƒ— = |โ– 8(๐‘– ฬ‚&๐‘— ฬ‚&๐‘˜ ฬ‚@1&โˆ’1&3@2&โˆ’7&1)| = ๐‘– ฬ‚ (โˆ’1 ร— 1 โˆ’ (โˆ’7) ร— 3) โˆ’ ๐‘— ฬ‚ (1 ร— 1 โˆ’ 2 ร— 3) + ๐‘˜ ฬ‚ (1 ร— โˆ’7 โˆ’ 2 ร— โˆ’1) = ๐‘– ฬ‚ (โˆ’1โˆ’(โˆ’21)) โˆ’ ๐‘— ฬ‚ (1 โˆ’ 6) + ๐‘˜ ฬ‚ (โˆ’7 โˆ’(โˆ’2)) = ๐‘– ฬ‚ (โˆ’1 + 21) โˆ’ ๐‘— ฬ‚ (โˆ’5) + ๐‘˜ ฬ‚ (โˆ’7 + 2) = 20 ๐’Š ฬ‚ + 5๐’‹ ฬ‚ โˆ’ 5๐’Œ ฬ‚ Magnitude of ๐‘Ž โƒ— ร— ๐‘ โƒ— = โˆš(202+52+(โˆ’5)2) |๐‘Ž โƒ—" ร— " ๐‘ โƒ— | = โˆš(400+25+25) = โˆš450 = โˆš(25ร—9ร—2) = 5 ร— 3 ร— โˆš2 = 15 โˆš2 Therefore, the area of parallelogram is 15โˆš๐Ÿ .

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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.