The scalar projection of the vector 3i ฬ‚-j ฬ‚-2k ฬ‚ ๐‘œ๐‘› ๐‘กℎ๐‘’ ๐‘ฃ๐‘’๐‘๐‘ก๐‘œ๐‘Ÿ i ฬ‚+2j ฬ‚-3k ฬ‚ is

(a) 7/√14  

(b) 7/14  

(c) 6/13  

(d) 7/2

 

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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

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