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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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