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Find the angle between the unit vectors aΒ Μ‚ π‘Žπ‘›π‘‘ bΒ Μ‚ , given that |aΒ Μ‚+bΒ Μ‚ | = 1

Find the angle between the unit vectors a and b, given that |a + b|=1

Question 12 - CBSE Class 12 Sample Paper for 2021 Boards - Part 2


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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.