Find the angle between the unit vectors a Μ‚ π‘Žπ‘›π‘‘ b Μ‚ , given that |a Μ‚+b Μ‚ | = 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 π‘Ž Μ‚ π‘Žπ‘›π‘‘ 𝑏 Μ‚ , given that |π‘Ž Μ‚+𝑏 Μ‚ | = 1 Given |π‘Ž Μ‚+𝑏 Μ‚ |=1 Squaring both sides |𝒂 Μ‚+𝒃 Μ‚ |^𝟐=𝟏^𝟐 |π‘Ž Μ‚ |^2+|𝑏 Μ‚ |^2+2π‘Ž Μ‚.𝑏 Μ‚=1 |𝒂 Μ‚ |^𝟐+|𝒃 Μ‚ |^𝟐+𝟐|𝒂 Μ‚|.|𝒃 Μ‚ | πœπ¨π¬β‘γ€–πœ½ γ€—=𝟏 Since π‘Ž Μ‚ and 𝑏 Μ‚ are unit vectors, |π‘Ž Μ‚ | = 1 and |𝑏 Μ‚ | = 1 𝟏^𝟐+𝟏^𝟐+𝟐 Γ— 𝟏 Γ— 𝟏 Γ—πœπ¨π¬β‘πœ½=𝟏 1+1+2 cos⁑θ=1 2+2 cos⁑θ=1 2 cos⁑θ=1βˆ’2 2 cos⁑θ=βˆ’1 π’„π’π’”β‘πœ½=(βˆ’πŸ)/𝟐 Thus, ΞΈ = 120Β° ΞΈ = πŸπ…/π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.