Question 12 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 14, 2026 by Teachoo

Find the angle between the unit vectors a ̂ 𝑎𝑛𝑑 b ̂ , given that |a ̂+b ̂ | = 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 𝑎 ̂ 𝑎𝑛𝑑 𝑏 ̂ , given that |𝑎 ̂+𝑏 ̂ | = 1 Given |𝑎 ̂+𝑏 ̂ |=1 Squaring both sides |𝒂 ̂+𝒃 ̂ |^𝟐=𝟏^𝟐 |𝑎 ̂ |^2+|𝑏 ̂ |^2+2𝑎 ̂.𝑏 ̂=1 |𝒂 ̂ |^𝟐+|𝒃 ̂ |^𝟐+𝟐|𝒂 ̂|.|𝒃 ̂ | 𝐜𝐨𝐬⁡〖𝜽 〗=𝟏 Since 𝑎 ̂ and 𝑏 ̂ are unit vectors, |𝑎 ̂ | = 1 and |𝑏 ̂ | = 1 𝟏^𝟐+𝟏^𝟐+𝟐 × 𝟏 × 𝟏 ×𝐜𝐨𝐬⁡𝜽=𝟏 1+1+2 cos⁡θ=1 2+2 cos⁡θ=1 2 cos⁡θ=1−2 2 cos⁡θ=−1 𝒄𝒐𝒔⁡𝜽=(−𝟏)/𝟐 Thus, θ = 120° θ = 𝟐𝝅/𝟑

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