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Example 24 - Find area of a triangle having A (1, 1, 1), B (1, 2, 3)

Example 24 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 24 Find the area of a triangle having the points A(1, 1, 1), B(1, 2, 3) and C(2, 3, 1) as its vertices. Given A (1, 1, 1) , B (1, 2, 3) ,C (2, 3, 1) Area of triangle ABC = 𝟏/𝟐 |(𝑨𝑩) βƒ— Γ— (𝑨π‘ͺ) βƒ— | Finding AB (𝑨𝑩) βƒ— = (1 βˆ’ 1) 𝑖 Μ‚ + (2 βˆ’ 1) 𝑗 Μ‚ + (3 βˆ’ 1) π‘˜ Μ‚ = 0𝑖 Μ‚ + 1𝑗 Μ‚ + 2π‘˜ Μ‚ Finding AC (𝑨π‘ͺ) βƒ— = (2 βˆ’ 1) 𝑖 Μ‚ + (3 βˆ’ 1) 𝑗 Μ‚ + (1 βˆ’ 1) π‘˜ Μ‚ = 1𝑖 Μ‚ + 2𝑗 Μ‚ + 0π‘˜ Μ‚ (𝑨𝑩) βƒ— Γ— (𝑨π‘ͺ) βƒ— = |β– 8(𝑖 Μ‚&𝑗 Μ‚&π‘˜ Μ‚@0&1&2@1&2&0)| = 𝑖 Μ‚ [(1Γ—0)βˆ’(2Γ—2)] βˆ’ 𝑗 Μ‚[(0Γ—0)βˆ’(1Γ—2)] + π‘˜ Μ‚[(0Γ—2)βˆ’(1Γ—1)] = βˆ’4π’Š Μ‚ + 2𝒋 Μ‚ – 1π’Œ Μ‚ Magnitude of (𝐴𝐡) βƒ— Γ— (𝐴𝐢) βƒ— = √((βˆ’4)2+22+(βˆ’1)2) |(𝑨𝑩) βƒ—" Γ— " (𝑨π‘ͺ) βƒ— | = √(16+4+1) = √𝟐𝟏 Therefore, Area of triangle ABC = 1/2 |(𝐴𝐡) βƒ—" Γ— " (𝐴𝐢) βƒ— | = 1/2 Γ— √21 = √𝟐𝟏/𝟐

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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.