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Ex 10.3
Ex 10.3, 2
Ex 10.3, 3 Important
Ex 10.3, 4 You are here
Ex 10.3, 5 Important
Ex 10.3, 6
Ex 10.3, 7
Ex 10.3, 8
Ex 10.3, 9 Important
Ex 10.3, 10 Important
Ex 10.3, 11
Ex 10.3, 12 Important
Ex 10.3, 13 Important
Ex 10.3, 14
Ex 10.3, 15 Important
Ex 10.3, 16 Important
Ex 10.3, 17
Ex 10.3, 18 (MCQ) Important
Last updated at March 30, 2023 by Teachoo
Ex 10.3, 4 Find the projection of the vector 𝑖 ̂ + 3𝑗 ̂ + 7𝑘 ̂ on the vector 7𝑖 ̂ - 𝑗 ̂ + 8𝑘 ̂ . Projection of vector 𝒂 ⃗ on 𝒃 ⃗ = 𝟏/|𝒃 ⃗ | (𝒂 ⃗. 𝒃 ⃗) Let 𝑎 ⃗ = 1𝑖 ̂ + 3𝑗 ̂ + 7𝑘 ̂ 𝑏 ⃗ = 7𝑖 ̂ – 1𝑗 ̂ + 8𝑘 ̂ (𝒂 ⃗ . 𝒃 ⃗) = (1 × 7) + (3 × −1) + (7 × 8) = 7 + (−3) + 56 = 60 Magnitude of 𝑏 ⃗ = √(72+(−1)2+82) |𝑏 ⃗ | = √(49+1+64) = √𝟏𝟏𝟒 Projection of 𝑎 ⃗ on 𝑏 ⃗ = 1/|𝑏 ⃗ | (𝑎 ⃗. 𝑏 ⃗) = 1/√114 × 60 = 60/√114 Thus projection of 𝑎 ⃗ on 𝑏 ⃗ = 𝟔𝟎/√𝟏𝟏𝟒