Last updated at May 6, 2021 by Teachoo

Transcript

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 = ๐/๐ |(๐จ๐ฉ) โ ร (๐จ๐ช) โ | Finding AB (๐จ๐ฉ) โ = (1 โ 1) ๐ ฬ + (2 โ 1) ๐ ฬ + (3 โ 1) ๐ ฬ = 0๐ ฬ + 1๐ ฬ + 2๐ ฬ Finding AC (๐จ๐ช) โ = (2 โ 1) ๐ ฬ + (3 โ 1) ๐ ฬ + (1 โ 1) ๐ ฬ = 1๐ ฬ + 2๐ ฬ + 0๐ ฬ (๐จ๐ฉ) โ ร (๐จ๐ช) โ = |โ 8(๐ ฬ&๐ ฬ&๐ ฬ@0&1&2@1&2&0)| = ๐ ฬ [(1ร0)โ(2ร2)] โ ๐ ฬ[(0ร0)โ(1ร2)] + ๐ ฬ[(0ร2)โ(1ร1)] = โ4๐ ฬ + 2๐ ฬ โ 1๐ ฬ Magnitude of (๐ด๐ต) โ ร (๐ด๐ถ) โ = โ((โ4)2+22+(โ1)2) |(๐จ๐ฉ) โ" ร " (๐จ๐ช) โ | = โ(16+4+1) = โ๐๐ Therefore, Area of triangle ABC = 1/2 |(๐ด๐ต) โ" ร " (๐ด๐ถ) โ | = 1/2 ร โ21 = โ๐๐/๐

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Example 24 You are here

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Example 26 (Supplementary NCERT) Deleted for CBSE Board 2022 Exams

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Example 28 (Supplementary NCERT) Important Deleted for CBSE Board 2022 Exams

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Example 31 (Supplementary NCERT) Important Deleted for CBSE Board 2022 Exams

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.