Ex 10.4, 11 - Let |a|= 3, |b| = root2/3, Then a x b is unit vector - Vector product - Defination

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Ex 10.4, 11 Let the vectors 𝑎﷯ and 𝑏﷯ be such that | 𝑎﷯| = 3 and | 𝑏﷯| = ﷮2﷯﷮3﷯, 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﷯﷯ = ﷮2﷯﷮3﷯ 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 × ﷮2﷯﷮3﷯ sin θ 1 = ﷮2﷯ sinθ sin θ = 1﷮ ﷮2﷯﷯ θ = sin-1 𝟏﷮ ﷮𝟐﷯﷯﷯ = 𝝅﷮𝟒﷯ Therefore, the angle between the vectors 𝑎﷯ and 𝑏﷯ is 𝝅﷮𝟒﷯ . Hence, (B) is the correct option

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