Example 16 - Chapter 10 Class 12 Vector Algebra
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 16 Find the projection of the vector 𝑎 ⃗ = 2𝑖 ̂ + 3𝑗 ̂ + 2𝑘 ̂ on the vector 𝑏 ⃗ = 𝑖 ̂ + 2𝑗 ̂ + 𝑘 ̂. Given 𝑎 ⃗ = 2𝑖 ̂ + 3𝑗 ̂ + 2𝑘 ̂ 𝑏 ⃗ = 1𝑖 ̂ + 2𝑗 ̂ + 1𝑘 ̂ We know that Projection of vector 𝑎 ⃗ on 𝑏 ⃗ = 𝟏/("|" 𝒃 ⃗"|" ) (𝑎 ⃗. 𝑏 ⃗) Finding 𝒂 ⃗. 𝒃 ⃗ (𝒂 ⃗. 𝒃 ⃗) = (2 × 1) + (3 × 2) + (2 × 1) = 2 + 6 + 2 = 10 Magnitude of 𝑏 ⃗ = √(12+22+12) |𝒃 ⃗ | = √(1+4+1) = √𝟔 Now, Projection of vector 𝑎 ⃗ on 𝑏 ⃗ = 1/("|" 𝑏 ⃗"|" ) (𝑎 ⃗. 𝑏 ⃗) = 1/√6 (10) = 10/√6 = 10/√6 × √6/√6 = 10/6 × √6 = 𝟓/𝟑 √𝟔
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo