Example 25 - Find area of a parallelogram whose a = 3i + j + 4k

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Example 25 - Chapter 10 Class 12 Vector Algebra - Part 2

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

Transcript

Example 25 Find the area of a parallelogram whose adjacent sides are given by the vectors (๐‘Ž ) โƒ— = 3๐‘– ฬ‚ + ๐‘— ฬ‚ + 4๐‘˜ ฬ‚ and ๐‘ โƒ— = ๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + ๐‘˜ ฬ‚ Given (๐’‚ ) โƒ— = 3๐‘– ฬ‚ + 1๐‘— ฬ‚ + 4๐‘˜ ฬ‚ ๐’ƒ โƒ— = 1๐‘– ฬ‚ โˆ’ 1๐‘— ฬ‚ + 1k ฬ‚ Area of parallelogram ABCD = |๐’‚ โƒ— ร— ๐’ƒ โƒ— | Now, (๐’‚ ) โƒ—ร— ๐’ƒ โƒ— = |โ– 8(๐‘– ฬ‚&๐‘— ฬ‚&๐‘˜ ฬ‚@3&1&4@1&โˆ’1&1)| = ๐‘– ฬ‚ (1 ร— 1 โ€“ (โˆ’1) ร— 4) โˆ’ ๐‘— ฬ‚ (3 ร— 1 โ€“ 1 ร— 4) + ๐‘˜ ฬ‚ (3 ร— โˆ’1 โˆ’ 1 ร— 1) = ๐‘– ฬ‚(1 โˆ’ (-4)) โˆ’ j ฬ‚ (3 โˆ’ 4) + ๐‘˜ ฬ‚ (โˆ’3 โˆ’1) = ๐‘– ฬ‚(1 + 4) โˆ’ j ฬ‚ (โˆ’1) + ๐‘˜ ฬ‚ (โˆ’4) = 5๐’Š ฬ‚ + ๐’‹ ฬ‚ โˆ’ 4๐’Œ ฬ‚ Magnitude of ๐‘Ž โƒ— ร— ๐‘ โƒ— = โˆš(52+1^2+(โˆ’4)2) |๐’‚ โƒ— ร— ๐’ƒ โƒ— | = โˆš(25+1+16) = โˆš๐Ÿ’๐Ÿ Area of parallelogram ABCD = |๐‘Ž โƒ— ร— ๐‘ โƒ— | = โˆš42 Therefore, the required area is โˆš๐Ÿ’๐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.