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Ex 10.3, 3 - Find projection of vector i - j on vector i + j

Ex 10.3, 3 - Chapter 10 Class 12 Vector Algebra - Part 2

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Ex 10.3, 3 Find the projection of the vector 𝑖 Μ‚ βˆ’ 𝑗 Μ‚ on the vector 𝑖 Μ‚ + 𝑗 Μ‚ .Let π‘Ž βƒ— = 𝑖 Μ‚ βˆ’ 𝑗 Μ‚ = 1𝑖 Μ‚ – 1𝑗 Μ‚ + 0π‘˜ Μ‚ 𝑏 βƒ— = 𝑖 Μ‚ + 𝑗 Μ‚ = 1𝑖 Μ‚ + 1𝑗 Μ‚ + 0π‘˜ Μ‚ Projector of vector 𝒂 βƒ— on 𝒃 βƒ— = 𝟏/|𝒃 βƒ— | (𝒂 βƒ— . 𝒃 βƒ—) Now, 𝒂 βƒ— . 𝒃 βƒ— = (1 Γ— 1) (βˆ’1 Γ— 1) + (0 Γ— 0) = 1 + (βˆ’1) + 0 = 0 Also, Magnitude of 𝑏 βƒ— = √(12+12+02) |𝑏 βƒ— | = √(1+1+0) = √2 Projection of π‘Ž βƒ— on 𝑏 βƒ— = 1/|𝑏 βƒ— | (π‘Ž βƒ— . 𝑏 βƒ—) = 1/√2 (0) = 0

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