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

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

You can download the question paper hereΒ  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 Μ‚ βˆ’ 𝑗 Μ‚ + π‘˜ Μ‚ on 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + π‘˜ Μ‚ Let a = 2𝑖 Μ‚ βˆ’ 𝑗 Μ‚ + π‘˜ Μ‚ and b = 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + π‘˜ Μ‚ We need to find Projection (vector) of π‘Ž βƒ— on 𝑏 βƒ— Theory We know that Projection of π‘Ž βƒ— on 𝑏 βƒ— = 1/("|" 𝑏 βƒ—"|" ) (π‘Ž βƒ—. 𝑏 βƒ—) But here, we are asked projection (vector) So, we multiply projection by 𝑏 βƒ—/|𝑏 βƒ— | Projection (vector) of π‘Ž βƒ— on 𝑏 βƒ— = 1/|𝑏 βƒ— | (π‘Ž βƒ—. 𝑏 βƒ—) Γ— 𝑏 βƒ—/|𝑏 βƒ— | = ((π‘Ž βƒ— . 𝑏 βƒ— ))/|𝑏 βƒ— |^2 Γ— 𝑏 βƒ— (𝒂 βƒ—. 𝒃 βƒ—) = (2 Γ— 1) + (–1 Γ— –2) + (1 Γ— 1) = 2 + 2 + 1 = 5 Magnitude of 𝑏 βƒ— = √(12+(βˆ’2)2+12) |𝑏 βƒ— | = √(1+4+1) = √6 Projection (vector) of 𝒂 βƒ— on 𝒃 βƒ— = ((π‘Ž βƒ— . 𝑏 βƒ— ))/|𝑏 βƒ— |^2 Γ— 𝑏 βƒ— = 5/(√6)^2 Γ— ( 𝑖 Μ‚ βˆ’ 2𝑗 Μ‚ + π‘˜ Μ‚) = πŸ“/πŸ” ( π’Š Μ‚ βˆ’ 2𝒋 Μ‚ + π’Œ Μ‚)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.