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Ex 10.4, 10 - Find area of parallelogram whose adjacent sides are

Ex 10.4, 10 - Chapter 10 Class 12 Vector Algebra - Part 2

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Ex 10.4, 10 Find the area of the parallelogram whose adjacent sides are determined by the vectors 𝑎 ⃗ = 𝑖 ̂ − 𝑗 ̂ + 3𝑘 ̂ and b = 2𝑖 ̂ − 7𝑗 ̂ + 𝑘 ̂ . 𝑎 ⃗ = 𝑖 ̂ − 𝑗 ̂ + 3𝑘 ̂ = 1𝑖 ̂ − 1𝑗 ̂ + 3k ̂ 𝑏 ⃗ = 2𝑖 ̂ − 7𝑗 ̂ + 𝑘 ̂ = 2𝑖 ̂ − 7𝑗 ̂ + 1k ̂ Area of parallelogram ABCD = |𝑎 ⃗" × " 𝑏 ⃗ | 𝒂 ⃗ × 𝒃 ⃗ = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@1&−1&3@2&−7&1)| = 𝑖 ̂ (−1 × 1 − (−7) × 3) − 𝑗 ̂ (1 × 1 − 2 × 3) + 𝑘 ̂ (1 × −7 − 2 × −1) = 𝑖 ̂ (−1−(−21)) − 𝑗 ̂ (1 − 6) + 𝑘 ̂ (−7 −(−2)) = 𝑖 ̂ (−1 + 21) − 𝑗 ̂ (−5) + 𝑘 ̂ (−7 + 2) = 20 𝒊 ̂ + 5𝒋 ̂ − 5𝒌 ̂ Magnitude of 𝑎 ⃗ × 𝑏 ⃗ = √(202+52+(−5)2) |𝑎 ⃗" × " 𝑏 ⃗ | = √(400+25+25) = √450 = √(25×9×2) = 5 × 3 × √2 = 15 √2 Therefore, the area of parallelogram is 15√𝟐 .

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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.