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Ex 10.4, 9 - Find area of triangle A(1, 1, 2), B(2, 3, 5)

Ex 10.4, 9 - Chapter 10 Class 12 Vector Algebra - Part 2


Transcript

Ex 10.4, 9 Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5). A (1, 1, 2) , B (2, 3, 5) , C (1, 5, 5) Area of triangle ABC is 1/2 |(𝐴𝐵) ⃗ × (𝐴𝐶) ⃗ | A (1, 1, 2) B (2, 3, 5) (𝐴𝐵) ⃗ = (2 − 1) 𝑖 ̂ + (3 − 1) 𝑗 ̂ + (5 − 2) 𝑘 ̂ = 1𝑖 ̂ + 2𝑗 ̂ + 3𝑘 ̂ A (1, 1, 2) C (1, 5, 5) (𝐴𝐶) ⃗ = (1 − 1) 𝑖 ̂ + (5 − 1) 𝑗 ̂ + (5 − 2) 𝑘 ̂ = 0𝑖 ̂ + 4𝑗 ̂ + 3𝑘 ̂ (𝑨𝑩) ⃗ × (𝑨𝑪) ⃗ = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@1&2&[email protected]&4&3)| = 𝑖 ̂ (2×3−4×3 )−𝑗 ̂ (1×3−0×3 )+𝑘 ̂ (1×4−0×2 ) = 𝑖 ̂ (6−12)−𝑗 ̂(3−0) + 𝑘 ̂ (4−0) = −6𝒊 ̂ – 3𝒋 ̂ + 4𝒌 ̂ Magnitude of (𝐴𝐵) ⃗ × (𝐴𝐶) ⃗ = √((−6)2+(−3)2+42) |(𝐴𝐵) ⃗" × " (𝐴𝐶) ⃗ | = √(36+9+16) = √61 Area of triangle ABC = 1/2 |(𝐴𝐵) ⃗" × " (𝐴𝐶) ⃗ | = 1/2 × √61 = √𝟔𝟏/𝟐

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.