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Ex 10.4, 10 - Chapter 10 Class 12 Vector Algebra
Last updated at May 29, 2023 by Teachoo
Transcript
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 .
