Ex 10.2, 9 - Chapter 10 Class 12 Vector Algebra (Important Question)

Last updated at December 16, 2024 by Teachoo

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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Transcript

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

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