CBSE Class 12 Sample Paper for 2021 Boards
You are here
CBSE Class 12 Sample Paper for 2021 Boards
Last updated at Dec. 16, 2024 by Teachoo
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
