Ex 10.2, 9 - For a = 2i - j + 2k, and b = -i + j - k, find unit vector

Ex 10.2, 9 - Chapter 10 Class 12 Vector Algebra - Part 2

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Ex 10.2, 9 For given vectors, 𝑎 ⃗ = 2𝑖 ̂ − 𝑗 ̂ + 2𝑘 ̂ and 𝑏 ⃗ = −𝑖 ̂ + 𝑗 ̂ − 𝑘 ̂ , find the unit vector in the direction of the vector 𝑎 ⃗ + 𝑏 ⃗𝑎 ⃗ = 2𝑖 ̂ − j ̂ + 2𝑘 ̂ = 2𝑖 ̂ – 1𝑗 ̂ + 2𝑘 ̂ 𝑏 ⃗ = −𝑖 ̂ + 𝑗 ̂ – 𝑘 ̂ = −1𝑖 ̂ + 1𝑗 ̂ – 1𝑘 ̂ Now, (𝑎 ⃗ + 𝑏 ⃗) = (2 – 1) 𝑖 ̂ + (-1 + 1) 𝑗 ̂ + (2 – 1) 𝑘 ̂ = 1𝑖 ̂ + 0𝑗 ̂ + 1𝑘 ̂ Let 𝑐 ⃗ = 𝑎 ⃗ + 𝑏 ⃗ ∴ c ⃗ = 1𝑖 ̂ + 0𝑗 ̂ + 1𝑘 ̂ Magnitude of 𝑐 ⃗ = √(12+02+12) |𝑐 ⃗ | = √(1+0+1) = √2 Unit vector in direction of 𝑐 ⃗ = 1/|𝑐 ⃗ | . 𝑐 ⃗ 𝑐 ̂ = 1/√2 [1𝑖 ̂+0𝑗 ̂+1𝑘 ̂ ] 𝑐 ̂ = 1/√2 𝑖 ̂ + 0𝑗 ̂ + 1/√2 𝑘 ̂ 𝑐 ̂ = 𝟏/√𝟐 𝒊 ̂ + 𝟏/√𝟐 𝒌 ̂ Thus, unit vector in direction of 𝑐 ⃗ = 1/√2 𝑖 ̂ + 1/√2 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