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Question 11 - CBSE Class 12 Sample Paper for 2018 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at March 16, 2023 by

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

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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.