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The scalar projection of the vector 3i ฬ‚-j ฬ‚-2k ฬ‚ ๐‘œ๐‘› ๐‘กโ„Ž๐‘’ ๐‘ฃ๐‘’๐‘๐‘ก๐‘œ๐‘Ÿ i ฬ‚+2j ฬ‚-3k ฬ‚ is

(a) 7/โˆš14 ย 

(b) 7/14 ย 

(c) 6/13 ย 

(d) 7/2

ย 

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Question 8 The scalar projection of the vector 3๐‘– ฬ‚โˆ’๐‘— ฬ‚โˆ’2๐‘˜ ฬ‚ ๐‘œ๐‘› ๐‘กโ„Ž๐‘’ ๐‘ฃ๐‘’๐‘๐‘ก๐‘œ๐‘Ÿ ๐‘– ฬ‚+2๐‘— ฬ‚โˆ’3๐‘˜ ฬ‚ is (a) 7/โˆš14 (b) 7/14 (c) 6/13 (d) 7/2 Let a = 3๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚ and b = ๐‘– ฬ‚ + 2๐‘— ฬ‚ โˆ’ 3๐‘˜ ฬ‚ We need to find Projection of ๐‘Ž โƒ— on ๐‘ โƒ— We know that Projection of ๐‘Ž โƒ— on ๐‘ โƒ— = ๐Ÿ/("|" ๐’ƒ โƒ—"|" ) (๐’‚ โƒ—. ๐’ƒ โƒ—) Now, (๐’‚ โƒ—. ๐’ƒ โƒ—) = (3๐‘– ฬ‚ โˆ’ ๐‘— ฬ‚ โˆ’ 2๐‘˜ ฬ‚ ) . (๐‘– ฬ‚ + 2๐‘— ฬ‚ โˆ’ 3๐‘˜ ฬ‚) = (3 ร— 1) + (โ€“1 ร— 2) + (โˆ’2 ร— โˆ’3) = 7 Magnitude of ๐‘ โƒ— = โˆš(12+22+(โˆ’3) 2) |๐’ƒ โƒ— | = โˆš(1+4+9) = โˆš๐Ÿ๐Ÿ’ Thus, Projection of ๐’‚ โƒ— on ๐’ƒ โƒ— = 1/("|" ๐‘ โƒ—"|" ) (๐‘Ž โƒ—. ๐‘ โƒ—) = ๐Ÿ•/โˆš๐Ÿ๐Ÿ’ So, the correct answer is (a)

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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.