Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.4, 11 Let the vectors 𝑎 and 𝑏 be such that | 𝑎| = 3 and | 𝑏| = 23, Then 𝑎 × 𝑏 is a unit vector, if the angle between 𝑎 and 𝑏 is (A) π/6 (B) π/4 (C) π/3 (D) π/2 𝑎 = 3 & 𝑏 = 23 𝑎 × 𝑏 = 𝑎 𝑏 sin θ 𝑛 Given, ( 𝑎 × 𝑏) is a unit vector Magnitude of ( 𝑎 × 𝑏) = | 𝒂 × 𝒃| = 1 Now, 𝒂 × 𝒃 = 𝒂 𝒃 sin θ 𝒏 , θ is the angle between 𝑎 and 𝑏. 𝑎 × 𝑏 = 𝑎 𝑏 sin θ 𝑛 𝑎 × 𝑏 = 𝑎 𝑏 sin θ × 1 𝑎 × 𝑏 = 𝑎 𝑏 sin θ 1 = 3 × 23 sin θ 1 = 2 sinθ sin θ = 1 2 θ = sin-1 𝟏 𝟐 = 𝝅𝟒 Therefore, the angle between the vectors 𝑎 and 𝑏 is 𝝅𝟒 . Hence, (B) is the correct option

About the Author

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.