Find the angle between the unit vectors a ฬ‚ ๐‘Ž๐‘›๐‘‘ b ฬ‚ , given that |a ฬ‚+b ฬ‚ | = 1

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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 12 Find the angle between the unit vectors ๐‘Ž ฬ‚ ๐‘Ž๐‘›๐‘‘ ๐‘ ฬ‚ , given that |๐‘Ž ฬ‚+๐‘ ฬ‚ | = 1 Given |๐‘Ž ฬ‚+๐‘ ฬ‚ |=1 Squaring both sides |๐’‚ ฬ‚+๐’ƒ ฬ‚ |^๐Ÿ=๐Ÿ^๐Ÿ |๐‘Ž ฬ‚ |^2+|๐‘ ฬ‚ |^2+2๐‘Ž ฬ‚.๐‘ ฬ‚=1 |๐’‚ ฬ‚ |^๐Ÿ+|๐’ƒ ฬ‚ |^๐Ÿ+๐Ÿ|๐’‚ ฬ‚|.|๐’ƒ ฬ‚ | ๐œ๐จ๐ฌโกใ€–๐œฝ ใ€—=๐Ÿ Since ๐‘Ž ฬ‚ and ๐‘ ฬ‚ are unit vectors, |๐‘Ž ฬ‚ | = 1 and |๐‘ ฬ‚ | = 1 ๐Ÿ^๐Ÿ+๐Ÿ^๐Ÿ+๐Ÿ ร— ๐Ÿ ร— ๐Ÿ ร—๐œ๐จ๐ฌโก๐œฝ=๐Ÿ 1+1+2 cosโกฮธ=1 2+2 cosโกฮธ=1 2 cosโกฮธ=1โˆ’2 2 cosโกฮธ=โˆ’1 ๐’„๐’๐’”โก๐œฝ=(โˆ’๐Ÿ)/๐Ÿ Thus, ฮธ = 120ยฐ ฮธ = ๐Ÿ๐…/๐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 9 years. He provides courses for Maths and Science at Teachoo.