Find the Projection (vector) of 2i − j + k on i − 2j + k

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/


Find Projection (vector) of 2i - j + k on i - 2j + k - Teachoo

Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Part 2
Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Part 3


Transcript

Question 11 Find the Projection (vector) of 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ on 𝑖 ̂ − 2𝑗 ̂ + 𝑘 ̂ Let a = 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ and b = 𝑖 ̂ − 2𝑗 ̂ + 𝑘 ̂ We need to find Projection (vector) of 𝑎 ⃗ on 𝑏 ⃗ Theory We know that Projection of 𝑎 ⃗ on 𝑏 ⃗ = 1/("|" 𝑏 ⃗"|" ) (𝑎 ⃗. 𝑏 ⃗) But here, we are asked projection (vector) So, we multiply projection by 𝑏 ⃗/|𝑏 ⃗ | Projection (vector) of 𝑎 ⃗ on 𝑏 ⃗ = 1/|𝑏 ⃗ | (𝑎 ⃗. 𝑏 ⃗) × 𝑏 ⃗/|𝑏 ⃗ | = ((𝑎 ⃗ . 𝑏 ⃗ ))/|𝑏 ⃗ |^2 × 𝑏 ⃗ (𝒂 ⃗. 𝒃 ⃗) = (2 × 1) + (–1 × –2) + (1 × 1) = 2 + 2 + 1 = 5 Magnitude of 𝑏 ⃗ = √(12+(−2)2+12) |𝑏 ⃗ | = √(1+4+1) = √6 Projection (vector) of 𝒂 ⃗ on 𝒃 ⃗ = ((𝑎 ⃗ . 𝑏 ⃗ ))/|𝑏 ⃗ |^2 × 𝑏 ⃗ = 5/(√6)^2 × ( 𝑖 ̂ − 2𝑗 ̂ + 𝑘 ̂) = 𝟓/𝟔 ( 𝒊 ̂ − 2𝒋 ̂ + 𝒌 ̂)

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