Last updated at March 11, 2017 by Teachoo

Transcript

Example 14 Find angle ‘θ’ between the vectors 𝑎 = 𝑖 + 𝑗 − 𝑘 and 𝑏 = 𝑖 − 𝑗 + 𝑘. 𝑎 = 𝑖 + 𝑗 − 𝑘 = 1 𝑖 + 1 𝑗 − 1 𝑘 𝑏 = 𝑖 – 𝑗 + 𝑘 = 1 𝑖 − 1 𝑗 + 1 𝑘 Magnitude of 𝑎 = 12+ 12+ −12 𝑎 = 1+1+1 = 3 Magnitude of 𝑏 = 12+(−1)2+12 𝑏 = 1+1+1 = 3 We know that , 𝑎 . 𝑏 = 𝑎 𝑏 cosθ 𝒂 . 𝒃 = (1 𝑖 + 1 𝑗 – 1 𝑘). (1 𝑖 − 1 𝑗 + 1 𝑘) = 1.1 + 1.(−1) + (−1)1 = 1 – 1 − 1 = −1 Now, 𝑎 . 𝑏 = 3 × 3 × cos θ −1 = 3 cos θ cos θ = −13 θ = cos−1 −𝟏𝟑 Therefore, the angle between 𝑎 and 𝑏 is cos-1 −13

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.