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

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

You can download the question paper here https://www.teachoo.com/cbse/sample-papers/

Last updated at Sept. 14, 2018 by Teachoo

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

You can download the question paper here https://www.teachoo.com/cbse/sample-papers/

Transcript

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