Ex 10.3, 8

Transcript

Ex 10.3, 8 Find the magnitude of two vectors 𝑎﷯ and 𝑏﷯, having the same magnitude and such that the angle between them is 60° and their scalar product is 1﷮2﷯ . Given, magnitude of two vectors 𝑎﷯ and 𝑏﷯ is same So, 𝑎﷯﷯ = 𝑏﷯﷯ We know that , 𝑎﷯ . 𝑏﷯ = 𝑎﷯﷯ 𝑏﷯﷯ cos θ , θ is the angle between 𝑎﷯ and 𝑏﷯ Given θ = 60° & 𝑎﷯ . 𝑏﷯ = 1﷮2﷯ Now, 𝑎﷯ . 𝑏﷯ = 𝑎﷯﷯ 𝑏﷯﷯ cos θ 𝑎﷯ . 𝑏﷯ = 𝑎﷯﷯ 𝑎﷯﷯ cos 60° 1﷮2﷯ = 𝑎﷯﷯2 × 1﷮2﷯ 𝑎﷯﷯2 = 1 𝑎﷯﷯ = ± 1 Since, magnitude of a vector is not negative, So, 𝑎﷯﷯ = 1 So 𝒂﷯﷯ = 𝒃﷯﷯ = 1 Thus, magnitude of 𝑎﷯ and 𝑏﷯ is 1.