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 April 16, 2024 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

Transcript

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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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