Question 11 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

Find the area of the triangle whose two sides are represented by the vectors 2i ̂ 𝑎𝑛𝑑 − 3j ̂.

Find area of the triangle whose two sides are vectors 2i and -3j

Question 11 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

Transcript

Question 11 Find the area of the triangle whose two sides are represented by the vectors 2𝑖 ̂ 𝑎𝑛𝑑 −3𝑗 ̂ We know that Area of triangle ABC = 1/2 |(𝐴𝐵) ⃗ × (𝐴𝐶) ⃗ | Here, (𝐴𝐵) ⃗ = 2𝑖 ̂ and (𝐴𝐶) ⃗ = −3𝑗 ̂ (𝑨𝑩) ⃗ × (𝑨𝑪) ⃗ = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@2&0&0@0&−3&0)| = 𝑖 ̂ [(0 × 0)−(−3 × 0)] − 𝑗 ̂[(2 × 0)−(0 × 0)] + 𝑘 ̂[(2 × −3)−(0 × 0)] = −6𝒌 ̂ Magnitude of (𝐴𝐵) ⃗ × (𝐴𝐶) ⃗ = |−6𝑘 ̂| = 6 So, area of triangle ABC = 1/2 |(𝐴𝐵) ⃗" × " (𝐴𝐶) ⃗ | = 1/2 × 6 = 3 square units

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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