Ex 10.3, 2 - Chapter 10 Class 12 Vector Algebra

Transcript

Ex 10.3, 2 Find the angle between the vectors 𝑖﷯ − 2 𝑗﷯ + 3 𝑘﷯ and 3 𝑖﷯ - 2 𝑗﷯ + 𝑘﷯ Let 𝑎﷯ = 𝑖﷯ − 2 𝑗﷯ + 3 𝑘﷯ = 1 𝑖﷯ − 2 𝑗﷯ + 3 𝑘﷯ and 𝑏﷯ = 3 𝑖﷯ − 2 𝑗﷯ + 𝑘﷯ = 3 𝑖﷯ − 2 𝑗﷯ + 1 𝑘﷯ We know that 𝑎﷯ . 𝑏﷯ = 𝑎﷯﷯ 𝑏﷯﷯ cos θ ; θ is the angle between 𝑎﷯ & 𝑏﷯ Now, 𝒂﷯. 𝒃﷯ = (1 𝑖﷯ − 2 𝑗﷯ + 3 𝑘﷯). (3 𝑖﷯ − 2 𝑗﷯ + 1 𝑘﷯) = 1.3 + (−2).(−2) + 3.1 = 3 + 4 + 3 = 10 Magnitude of 𝑎﷯ = ﷮12+ −2﷯2+32﷯ 𝑎﷯﷯= ﷮1+4+9﷯ = ﷮14﷯ Magnitude of 𝑏﷯ = ﷮32+ −2﷯2+12﷯ 𝑏﷯﷯= ﷮9+4+1﷯ = ﷮14﷯ Now, 𝑎﷯ . 𝑏﷯ = 𝑎﷯﷯ 𝑏﷯﷯ cos θ 10 = ﷮14﷯ × ﷮14﷯ x cos θ 10 = 14 × cos θ cos θ = 10﷮14﷯ θ = cos-1 𝟓﷮𝟕﷯﷯ Thus, the angle between 𝑎﷯ and 𝑏﷯ is cos-1 5﷮7﷯﷯