Last updated at May 29, 2018 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. A (1, 1, 1) , B (1, 2, 3) ,C (2, 3, 1) The area of triangle ABC is 12 𝐴𝐵× 𝐴𝐶 𝑨𝑩 × 𝑨𝑪 = 𝑖 𝑗 𝑘012120 = 𝑖 1×0−(2×2) − 𝑗 0×0−(1×2) + 𝑘 0×2−(1×1) = −4 𝒊 + 2 𝒋 – 1 𝒌 Magnitude of 𝐴𝐵 × 𝐴𝐶 = −42+22+ −12 𝐴𝐵 × 𝐴𝐶 = 16+4+1 = 21 So, area of triangle ABC = 12 𝐴𝐵 × 𝐴𝐶 = 12 × 21 = 212 Therefore, the required area is 𝟐𝟏𝟐

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.