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Find the projection of the vector a = 2i + 3j + 2k on vector b=i+2j+k

Example 16 - Chapter 10 Class 12 Vector Algebra - Part 2

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Example 16 Find the projection of the vector π‘Ž βƒ— = 2𝑖 Μ‚ + 3𝑗 Μ‚ + 2π‘˜ Μ‚ on the vector 𝑏 βƒ— = 𝑖 Μ‚ + 2𝑗 Μ‚ + π‘˜ Μ‚. Given π‘Ž βƒ— = 2𝑖 Μ‚ + 3𝑗 Μ‚ + 2π‘˜ Μ‚ 𝑏 βƒ— = 1𝑖 Μ‚ + 2𝑗 Μ‚ + 1π‘˜ Μ‚ We know that Projection of vector π‘Ž βƒ— on 𝑏 βƒ— = 𝟏/("|" 𝒃 βƒ—"|" ) (π‘Ž βƒ—. 𝑏 βƒ—) Finding 𝒂 βƒ—. 𝒃 βƒ— (𝒂 βƒ—. 𝒃 βƒ—) = (2 Γ— 1) + (3 Γ— 2) + (2 Γ— 1) = 2 + 6 + 2 = 10 Magnitude of 𝑏 βƒ— = √(12+22+12) |𝒃 βƒ— | = √(1+4+1) = βˆšπŸ” Now, Projection of vector π‘Ž βƒ— on 𝑏 βƒ— = 1/("|" 𝑏 βƒ—"|" ) (π‘Ž βƒ—. 𝑏 βƒ—) = 1/√6 (10) = 10/√6 = 10/√6 Γ— √6/√6 = 10/6 Γ— √6 = πŸ“/πŸ‘ βˆšπŸ”

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.