The magnitude of projection of  (2i − j + k ) on (i − 2j + 2k ) is _______

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Question 15 (OR 1st Question) The magnitude of projection of (2𝑖 Μ‚ βˆ’ 𝑗 Μ‚ + π‘˜ Μ‚) on (𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + 2π‘˜ Μ‚) is _______ Projection of vector 𝒂 βƒ— on 𝒃 βƒ— = 𝟏/|𝒃 βƒ— | (𝒂 βƒ—. 𝒃 βƒ—) Let π‘Ž βƒ— = 2𝑖 Μ‚ – 𝑗 Μ‚ + π‘˜ Μ‚ 𝑏 βƒ— = 𝑖 Μ‚ – 2𝑗 Μ‚ + 2π‘˜ Μ‚ (𝒂 βƒ— . 𝒃 βƒ—) = (2 Γ— 1) + (–1 Γ— βˆ’2) + (1 Γ— 2) = 2 + 2 + 2 = 6 Magnitude of 𝑏 βƒ— = √(12+(βˆ’2)2+22) |𝑏 βƒ— | = √(1+4+4) |𝑏 βƒ— | = √9 |𝑏 βƒ— | = 3 Projection of π‘Ž βƒ— on 𝑏 βƒ— = 1/|𝑏 βƒ— | (π‘Ž βƒ—. 𝑏 βƒ—) = 1/3 Γ— 6 = 2 ∴ Magnitude of projection is 2 units Note: 1/2 marks will be deducted if you don’t write units

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.