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/


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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‚)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.