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Example 8 - Find unit vector in direction of sum of vectors

Example 8 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 8 Find the unit vector in the direction of the sum of the vectors, π‘Ž βƒ— = 2𝑖 Μ‚ + 2 𝑗 Μ‚ – 5π‘˜ Μ‚ and 𝑏 βƒ— = 2𝑖 Μ‚ + 𝑗 Μ‚ + 3π‘˜ Μ‚ Given 𝒂 βƒ— = 2𝑖 Μ‚ + 2𝑗 Μ‚ – 5π‘˜ Μ‚ 𝒃 βƒ— = 2𝑖 Μ‚ + 1𝑗 Μ‚ + 3π‘˜ Μ‚ Let 𝒄 βƒ— = (𝒂 βƒ— + 𝒃 βƒ—) = (2 + 2) 𝑖 Μ‚ + (2 + 1) 𝑗 Μ‚ + (–5 + 3) π‘˜ Μ‚ = 4𝑖 Μ‚ + 3𝑗 Μ‚ – 2π‘˜ Μ‚ ∴ 𝒄 βƒ— = 4π’Š Μ‚ + 3𝒋 Μ‚ – 2π’Œ Μ‚ Magnitude of 𝑐 βƒ— = √(42+32+(βˆ’2)2) |𝒄 βƒ— | = √(16+9+4) = βˆšπŸπŸ— Unit vector in direction of 𝑐 βƒ— = 𝟏/|𝒄 βƒ— | 𝒄 βƒ— 𝑐 Μ‚ = 1/√29 ["4" 𝑖 Μ‚" + 3" 𝑗 Μ‚" βˆ’ 2" π‘˜ Μ‚ ] 𝑐 Μ‚ = 4/√29 𝑖 Μ‚" " + 3/√29 𝑗 Μ‚" "– 2/√29 π‘˜ Μ‚" " Thus, Required unit vector = πŸ’/βˆšπŸπŸ— π’Š Μ‚" " + πŸ‘/βˆšπŸπŸ— 𝒋 Μ‚" "– 𝟐/βˆšπŸπŸ— π’Œ Μ‚

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