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Area of parallelogram whose diagonal vectors are given - Vector produc

Area of parallelogram whose diagonal vectors are given - Part 2
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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— |

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.