Example 8 - Chapter 10 Class 12 Vector Algebra
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 8 Find the unit vector in the direction of the sum of the vectors, 𝑎 ⃗ = 2𝑖 ̂ + 2 𝑗 ̂ – 5𝑘 ̂ and 𝑏 ⃗ = 2𝑖 ̂ + 𝑗 ̂ + 3𝑘 ̂ Given 𝒂 ⃗ = 2𝑖 ̂ + 2𝑗 ̂ – 5𝑘 ̂ 𝒃 ⃗ = 2𝑖 ̂ + 1𝑗 ̂ + 3𝑘 ̂ Let 𝒄 ⃗ = (𝒂 ⃗ + 𝒃 ⃗) = (2 + 2) 𝑖 ̂ + (2 + 1) 𝑗 ̂ + (–5 + 3) 𝑘 ̂ = 4𝑖 ̂ + 3𝑗 ̂ – 2𝑘 ̂ ∴ 𝒄 ⃗ = 4𝒊 ̂ + 3𝒋 ̂ – 2𝒌 ̂ Magnitude of 𝑐 ⃗ = √(42+32+(−2)2) |𝒄 ⃗ | = √(16+9+4) = √𝟐𝟗 Unit vector in direction of 𝑐 ⃗ = 𝟏/|𝒄 ⃗ | 𝒄 ⃗ 𝑐 ̂ = 1/√29 ["4" 𝑖 ̂" + 3" 𝑗 ̂" − 2" 𝑘 ̂ ] 𝑐 ̂ = 4/√29 𝑖 ̂" " + 3/√29 𝑗 ̂" "– 2/√29 𝑘 ̂" " Thus, Required unit vector = 𝟒/√𝟐𝟗 𝒊 ̂" " + 𝟑/√𝟐𝟗 𝒋 ̂" "– 𝟐/√𝟐𝟗 𝒌 ̂
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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 and Computer Science at Teachoo