Find the projection of the vector a = 2i + 3j + 2k on vector b=i+2j+k

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Example 16 - Chapter 10 Class 12 Vector Algebra - Part 2

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  1. Chapter 10 Class 12 Vector Algebra (Term 2)
  2. Serial order wise

Transcript

Example 16 Find the projection of the vector ๐‘Ž โƒ— = 2๐‘– ฬ‚ + 3๐‘— ฬ‚ + 2๐‘˜ ฬ‚ on the vector ๐‘ โƒ— = ๐‘– ฬ‚ + 2๐‘— ฬ‚ + ๐‘˜ ฬ‚. Given ๐‘Ž โƒ— = 2๐‘– ฬ‚ + 3๐‘— ฬ‚ + 2๐‘˜ ฬ‚ ๐‘ โƒ— = 1๐‘– ฬ‚ + 2๐‘— ฬ‚ + 1๐‘˜ ฬ‚ We know that Projection of vector ๐‘Ž โƒ— on ๐‘ โƒ— = ๐Ÿ/("|" ๐’ƒ โƒ—"|" ) (๐‘Ž โƒ—. ๐‘ โƒ—) Finding ๐’‚ โƒ—. ๐’ƒ โƒ— (๐’‚ โƒ—. ๐’ƒ โƒ—) = (2 ร— 1) + (3 ร— 2) + (2 ร— 1) = 2 + 6 + 2 = 10 Magnitude of ๐‘ โƒ— = โˆš(12+22+12) |๐’ƒ โƒ— | = โˆš(1+4+1) = โˆš๐Ÿ” Now, Projection of vector ๐‘Ž โƒ— on ๐‘ โƒ— = 1/("|" ๐‘ โƒ—"|" ) (๐‘Ž โƒ—. ๐‘ โƒ—) = 1/โˆš6 (10) = 10/โˆš6 = 10/โˆš6 ร— โˆš6/โˆš6 = 10/6 ร— โˆš6 = ๐Ÿ“/๐Ÿ‘ โˆš๐Ÿ”

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.