The magnitude of projection of  (2i − j + k ) on (i − 2j + 2k ) is _______

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Transcript

Question 15 (OR 1st Question) The magnitude of projection of (2๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ + ๐‘˜ ฬ‚) on (๐‘– ฬ‚ โˆ’ 2๐‘— ฬ‚ + 2๐‘˜ ฬ‚) is _______ Projection of vector ๐’‚ โƒ— on ๐’ƒ โƒ— = ๐Ÿ/|๐’ƒ โƒ— | (๐’‚ โƒ—. ๐’ƒ โƒ—) Let ๐‘Ž โƒ— = 2๐‘– ฬ‚ โ€“ ๐‘— ฬ‚ + ๐‘˜ ฬ‚ ๐‘ โƒ— = ๐‘– ฬ‚ โ€“ 2๐‘— ฬ‚ + 2๐‘˜ ฬ‚ (๐’‚ โƒ— . ๐’ƒ โƒ—) = (2 ร— 1) + (โ€“1 ร— โˆ’2) + (1 ร— 2) = 2 + 2 + 2 = 6 Magnitude of ๐‘ โƒ— = โˆš(12+(โˆ’2)2+22) |๐‘ โƒ— | = โˆš(1+4+4) |๐‘ โƒ— | = โˆš9 |๐‘ โƒ— | = 3 Projection of ๐‘Ž โƒ— on ๐‘ โƒ— = 1/|๐‘ โƒ— | (๐‘Ž โƒ—. ๐‘ โƒ—) = 1/3 ร— 6 = 2 โˆด Magnitude of projection is 2 units

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.