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Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Find the area of the triangle whose two sides are represented by the vectors 2iΒ Μ‚ π‘Žπ‘›π‘‘ βˆ’ 3jΒ Μ‚.

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

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Question 11 Find the area of the triangle whose two sides are represented by the vectors 2𝑖 Μ‚ π‘Žπ‘›π‘‘ βˆ’3𝑗 Μ‚ We know that Area of triangle ABC = 1/2 |(𝐴𝐡) βƒ— Γ— (𝐴𝐢) βƒ— | Here, (𝐴𝐡) βƒ— = 2𝑖 Μ‚ and (𝐴𝐢) βƒ— = βˆ’3𝑗 Μ‚ (𝑨𝑩) βƒ— Γ— (𝑨π‘ͺ) βƒ— = |β– 8(𝑖 Μ‚&𝑗 Μ‚&π‘˜ Μ‚@2&0&0@0&βˆ’3&0)| = 𝑖 Μ‚ [(0 Γ— 0)βˆ’(βˆ’3 Γ— 0)] βˆ’ 𝑗 Μ‚[(2 Γ— 0)βˆ’(0 Γ— 0)] + π‘˜ Μ‚[(2 Γ— βˆ’3)βˆ’(0 Γ— 0)] = βˆ’6π’Œ Μ‚ Magnitude of (𝐴𝐡) βƒ— Γ— (𝐴𝐢) βƒ— = |βˆ’6π‘˜ Μ‚| = 6 So, area of triangle ABC = 1/2 |(𝐴𝐡) βƒ—" Γ— " (𝐴𝐢) βƒ— | = 1/2 Γ— 6 = 3 square units

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