Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors i ฬ‚ - j ฬ‚ + k ฬ‚ and 4i ฬ‚ + 5k ฬ‚

 

Find area of the parallelogram whose one side and a diagonal are

Question 26 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

 

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 26 Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors ๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + ๐‘˜ ฬ‚ and 4๐‘– ฬ‚ + 5๐‘˜ ฬ‚ Let ABCD be the parallelogram Where ๐’‚ โƒ— = ๐’Š ฬ‚ โˆ’ ๐’‹ ฬ‚ + ๐’Œ ฬ‚ And Diagonal ๐‘‘ โƒ— = 4๐‘– ฬ‚ + 5๐‘˜ ฬ‚ Now, ๐’‚ โƒ— + ๐’ƒ โƒ— = ๐’… โƒ— ๐‘ โƒ— = ๐‘‘ โƒ— โˆ’ ๐‘Ž โƒ— ๐‘ โƒ— = (4๐‘– ฬ‚ + 5๐‘˜ ฬ‚ ) โˆ’ (๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + ๐‘˜ ฬ‚ ) ๐’ƒ โƒ— = 3๐’Š ฬ‚ + ๐’‹ ฬ‚ + 4๐’Œ ฬ‚ Now, 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&1@3&1&4)| = ๐‘– ฬ‚ (โˆ’1 ร— 4 โˆ’ 1 ร— 1) โˆ’ ๐‘— ฬ‚ (1 ร— 4 โˆ’ 3 ร— 1) + ๐‘˜ ฬ‚ (1 ร— 1 โˆ’ 3 ร— โˆ’1) = ๐‘– ฬ‚ (โˆ’4 โˆ’ 1) โˆ’ ๐‘— ฬ‚ (4 โˆ’ 3) + ๐‘˜ ฬ‚ (1 + 3) = โˆ’5๐’Š ฬ‚ โˆ’ ๐’‹ ฬ‚ + 4๐’Œ ฬ‚ Now, Area of Parallelogram ABCD = |(๐‘จ๐‘ฉ) โƒ— ร— (๐‘ฉ๐‘ช) โƒ— | = โˆš((โˆ’5)2+(โˆ’1)2+42) = โˆš(25+1+16) = โˆš๐Ÿ’๐Ÿ square units

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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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.