Last updated at Dec. 24, 2019 by Teachoo

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+ −22+32 𝑎= 1+4+9 = 14 Magnitude of 𝑏 = 32+ −22+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 = 1014 θ = cos-1 𝟓𝟕 Thus, the angle between 𝑎 and 𝑏 is cos-1 57

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.