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Question 10 (OR 1 st question)

Find the area of the parallelogram whose diagonals are represented by the vectors a = 2iΒ  – 3jΒ  + 4k and b = 2i – j + 2k

We use the Area of Parallelogram formula with Diagonals

Find area of parallelogram by vectors a = 2i – 3jΒ  + 4k and b = 2i - j

Question 10 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 2
Question 10 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards - Part 3


Transcript

Question 10 (OR 1st question) Find the area of the parallelogram whose diagonals are represented by the vectors π‘Ž βƒ— = 2𝑖 Μ‚ – 3𝑗 Μ‚ + 4π‘˜ Μ‚ and 𝑏 βƒ— = 2𝑖 Μ‚ – 𝑗 Μ‚ + 2π‘˜ Μ‚ Area of parallelogram with diagonals Area = 1/2 |(𝑑_1 ) βƒ—Γ—(𝑑_2 ) βƒ— | Given Diagonals of a parallelogram as π‘Ž βƒ— = 2𝑖 Μ‚ – 3𝑗 Μ‚ + 4π‘˜ Μ‚ and 𝑏 βƒ— = 2𝑖 Μ‚ – 𝑗 Μ‚ + 2π‘˜ Μ‚ Area of the parallelogram = 1/2 |π‘Ž ⃗×𝑏 βƒ— | Finding 𝒂 βƒ— Γ— 𝒃 βƒ— π‘Ž βƒ— Γ— 𝑏 βƒ— = |β– 8(𝑖 Μ‚&𝑗 Μ‚&π‘˜ Μ‚@2&βˆ’3&4@2&βˆ’1&2)| = 𝑖 Μ‚ ((–3) Γ— 2 – (-1) Γ— 4) βˆ’ 𝑗 Μ‚ (2 Γ— 2 βˆ’ 2 Γ— 4) + π‘˜ Μ‚ (2 Γ— (-1) βˆ’ 2 Γ— (-3)) = 𝑖 Μ‚ (-6 + 4) βˆ’ 𝑗 Μ‚ (4 – 8) + π‘˜ Μ‚ (–2 + 6) = 𝑖 Μ‚ (βˆ’2) - 𝑗 Μ‚ (βˆ’4) + π‘˜ Μ‚ (4) = –2𝑖 Μ‚ + 4𝑗 Μ‚ + 4π‘˜ Μ‚ So, Magnitude of π‘Ž βƒ— Γ— 𝑏 βƒ— = √((βˆ’2)2+(4)2+(4)2) |π‘Ž βƒ—" Γ— " 𝑏 βƒ— | = √(4+16+16) |π‘Ž βƒ—" Γ— " 𝑏 βƒ— |= √36 |π‘Ž βƒ—" Γ— " 𝑏 βƒ— |= 6 Thus, Area of the parallelogram = 1/2 |π‘Ž ⃗×𝑏 βƒ— | = 1/2 Γ— 6 = 3 square units

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Davneet Singh

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.