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

Go Ad-free

Transcript

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

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.