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Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors iΒ Μ‚ - jΒ Μ‚ + kΒ Μ‚ and 4iΒ Μ‚ + 5kΒ Μ‚

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

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

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Question 26 Find the area of the parallelogram whose one side and a diagonal are represented by conitial vectors 𝑖 Μ‚ βˆ’ 𝑗 Μ‚ + π‘˜ Μ‚ and 4𝑖 Μ‚ + 5π‘˜ Μ‚ Let ABCD be the parallelogram Where 𝒂 βƒ— = π’Š Μ‚ βˆ’ 𝒋 Μ‚ + π’Œ Μ‚ And Diagonal 𝑑 βƒ— = 4𝑖 Μ‚ + 5π‘˜ Μ‚ Now, 𝒂 βƒ— + 𝒃 βƒ— = 𝒅 βƒ— 𝑏 βƒ— = 𝑑 βƒ— βˆ’ π‘Ž βƒ— 𝑏 βƒ— = (4𝑖 Μ‚ + 5π‘˜ Μ‚ ) βˆ’ (𝑖 Μ‚ βˆ’ 𝑗 Μ‚ + π‘˜ Μ‚ ) 𝒃 βƒ— = 3π’Š Μ‚ + 𝒋 Μ‚ + 4π’Œ Μ‚ Now, Area of parallelogram ABCD = |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | 𝒂 βƒ— Γ— 𝒃 βƒ— = |β– 8(𝑖 Μ‚&𝑗 Μ‚&π‘˜ Μ‚@1&βˆ’1&1@3&1&4)| = 𝑖 Μ‚ (βˆ’1 Γ— 4 βˆ’ 1 Γ— 1) βˆ’ 𝑗 Μ‚ (1 Γ— 4 βˆ’ 3 Γ— 1) + π‘˜ Μ‚ (1 Γ— 1 βˆ’ 3 Γ— βˆ’1) = 𝑖 Μ‚ (βˆ’4 βˆ’ 1) βˆ’ 𝑗 Μ‚ (4 βˆ’ 3) + π‘˜ Μ‚ (1 + 3) = βˆ’5π’Š Μ‚ βˆ’ 𝒋 Μ‚ + 4π’Œ Μ‚ Now, Area of Parallelogram ABCD = |(𝑨𝑩) βƒ— Γ— (𝑩π‘ͺ) βƒ— | = √((βˆ’5)2+(βˆ’1)2+42) = √(25+1+16) = βˆšπŸ’πŸ square units

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.