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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 Dec. 16, 2024 by Teachoo

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/

Transcript

Question 11 Find the Projection (vector) of 2๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + ๐‘˜ ฬ‚ on ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + ๐‘˜ ฬ‚ Let a = 2๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + ๐‘˜ ฬ‚ and b = ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + ๐‘˜ ฬ‚ We need to find Projection (vector) of ๐‘Ž โƒ— on ๐‘ โƒ— Theory We know that Projection of ๐‘Ž โƒ— on ๐‘ โƒ— = 1/("|" ๐‘ โƒ—"|" ) (๐‘Ž โƒ—. ๐‘ โƒ—) But here, we are asked projection (vector) So, we multiply projection by ๐‘ โƒ—/|๐‘ โƒ— | Projection (vector) of ๐‘Ž โƒ— on ๐‘ โƒ— = 1/|๐‘ โƒ— | (๐‘Ž โƒ—. ๐‘ โƒ—) ร— ๐‘ โƒ—/|๐‘ โƒ— | = ((๐‘Ž โƒ— . ๐‘ โƒ— ))/|๐‘ โƒ— |^2 ร— ๐‘ โƒ— (๐’‚ โƒ—. ๐’ƒ โƒ—) = (2 ร— 1) + (โ€“1 ร— โ€“2) + (1 ร— 1) = 2 + 2 + 1 = 5 Magnitude of ๐‘ โƒ— = โˆš(12+(โˆ’2)2+12) |๐‘ โƒ— | = โˆš(1+4+1) = โˆš6 Projection (vector) of ๐’‚ โƒ— on ๐’ƒ โƒ— = ((๐‘Ž โƒ— . ๐‘ โƒ— ))/|๐‘ โƒ— |^2 ร— ๐‘ โƒ— = 5/(โˆš6)^2 ร— ( ๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + ๐‘˜ ฬ‚) = ๐Ÿ“/๐Ÿ” ( ๐’Š ฬ‚ โˆ’ 2๐’‹ ฬ‚ + ๐’Œ ฬ‚)
  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo