Example 16 - Chapter 10 Class 12 Vector Algebra

Last updated at August 11, 2026 by

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

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

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Example 16 Find the projection of the vector š‘Ž āƒ— = 2š‘– Ģ‚ + 3š‘— Ģ‚ + 2š‘˜ Ģ‚ on the vector š‘ āƒ— = š‘– Ģ‚ + 2š‘— Ģ‚ + š‘˜ Ģ‚. Given š‘Ž āƒ— = 2š‘– Ģ‚ + 3š‘— Ģ‚ + 2š‘˜ Ģ‚ š‘ āƒ— = 1š‘– Ģ‚ + 2š‘— Ģ‚ + 1š‘˜ Ģ‚ We know that Projection of vector š‘Ž āƒ— on š‘ āƒ— = šŸ/("|" š’ƒ āƒ—"|" ) (š‘Ž āƒ—. š‘ āƒ—) Finding š’‚ āƒ—. š’ƒ āƒ— (š’‚ āƒ—. š’ƒ āƒ—) = (2 Ɨ 1) + (3 Ɨ 2) + (2 Ɨ 1) = 2 + 6 + 2 = 10 Magnitude of š‘ āƒ— = āˆš(12+22+12) |š’ƒ āƒ— | = āˆš(1+4+1) = āˆššŸ” Now, Projection of vector š‘Ž āƒ— on š‘ āƒ— = 1/("|" š‘ āƒ—"|" ) (š‘Ž āƒ—. š‘ āƒ—) = 1/āˆš6 (10) = 10/āˆš6 = 10/āˆš6 Ɨ āˆš6/āˆš6 = 10/6 Ɨ āˆš6 = šŸ“/šŸ‘ āˆššŸ”

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