### Find the Projection (vector) of 2i − j + k on i − 2j + k

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Last updated at May 29, 2018 by Teachoo

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Question 11 Find the Projection (vector) of 2๐ย ฬ โ ๐ย ฬ + ๐ย ฬ on ๐ย ฬ โ 2๐ย ฬ + ๐ย ฬ Let a = 2๐ย ฬ โ ๐ย ฬ + ๐ย ฬ and b = ๐ย ฬ โ 2๐ย ฬ + ๐ย ฬ We need to find Projection (vector) of ๐ย โ on ๐ย โ Theory We know thatProjection of ๐ย โ on ๐ย โ = 1/("|" ๐ย โ"|" ) (๐ย โ. ๐ย โ) But here, we are asked projection (vector) So, we multiply projection by ๐ย โ/|๐ย โ | Projection (vector) of ๐ย โ on ๐ย โ = 1/|๐ย โ | (๐ย โ. ๐ย โ) ร ๐ย โ/|๐ย โ | = ((๐ย โ . ๐ย โ ))/|๐ย โ |^2 ร ๐ย โ (๐ย โ. ๐ย โ) = (2 ร 1) + (โ1 ร โ2) + (1 ร 1) = 2 + 2 + 1 = 5 Magnitude of ๐ย โ = โ(12+(โ2)2+12) |๐ย โ | = โ(1+4+1) = โ6 Projection (vector) of ๐ย โ on ๐ย โ = ((๐ย โ . ๐ย โ ))/|๐ย โ |^2 ร ๐ย โ = 5/(โ6)^2 ร ( ๐ย ฬ โ 2๐ย ฬ + ๐ย ฬ) = ๐/๐ ( ๐ย ฬ โ 2๐ย ฬ + ๐ย ฬ)

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Class 12

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.