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https://www.teachoo.com/9020/2863/Question-10-(Or-1st)/category/CBSE-Class-12-Sample-Paper-for-2019-Boards/

  1. Chapter 10 Class 12 Vector Algebra
  2. Concept wise
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Transcript

Area of parallelogram whose diagonals are given Let us consider a parallelogram ABCD Here, π‘Ž βƒ— + 𝑏 βƒ— = (𝑑_1 ) βƒ— and 𝑏 βƒ— + (β€“π‘Ž βƒ—) = (𝑑_2 ) βƒ— 𝑏 βƒ— – π‘Ž βƒ— = (𝑑_2 ) βƒ— Let’s find (𝑑_1 ) βƒ— Γ— (𝑑_2 ) βƒ— (𝑑_1 ) βƒ— Γ— (𝑑_2 ) βƒ— = (π‘Ž βƒ— + 𝑏 βƒ—) Γ— (𝑏 βƒ— – π‘Ž βƒ—) = π‘Ž βƒ— Γ— (𝑏 βƒ— – π‘Ž βƒ—) + 𝑏 βƒ— Γ— (𝑏 βƒ— – π‘Ž βƒ—) = π‘Ž βƒ— Γ— 𝑏 βƒ— – π‘Ž βƒ— Γ— π‘Ž βƒ— + 𝑏 βƒ— Γ— 𝑏 βƒ— – 𝑏 βƒ— Γ— π‘Ž βƒ— Since π‘Ž βƒ— Γ— π‘Ž βƒ— = 0 = π‘Ž βƒ— Γ— 𝑏 βƒ— – 0 + 0 – 𝑏 βƒ— Γ— π‘Ž βƒ— = π‘Ž βƒ— Γ— 𝑏 βƒ— – 𝑏 βƒ— Γ— π‘Ž βƒ— Since 𝑏 βƒ— Γ— π‘Ž βƒ— = – (π‘Ž βƒ— Γ— 𝑏 βƒ—) = π‘Ž βƒ— Γ— 𝑏 βƒ— – (– (π‘Ž βƒ— Γ— 𝑏 βƒ—)) = (π‘Ž βƒ— Γ— 𝑏 βƒ—) + (π‘Ž βƒ— Γ— 𝑏 βƒ—) = 2 (π‘Ž βƒ— Γ— 𝑏 βƒ—) Therefore, (𝑑_1 ) βƒ— Γ— (𝑑_2 ) βƒ— = 2 (π‘Ž βƒ— Γ— 𝑏 βƒ—) Now, we know that Area of parallelogram = |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | Writing in terms of diagonals Area of parallelogram = 𝟏/𝟐 |(𝒅_𝟏 ) βƒ—Γ—(𝒅_𝟐 ) βƒ— |

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.