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Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.3, 12 (Introduction) If 𝑎 . 𝑎 = 0 and 𝑎 . 𝑏 = 0, then what can be concluded about the vector 𝑏 ? 𝑎 . 𝑏 = 𝑎 𝑏 cos θ , θ in the angle b/w 𝑎 and 𝑏 Let 𝑎 = 0 = 0 𝑖 + 0 𝑗 + 0 𝑘 Ex 10.3, 12 If 𝑎 . 𝑎 = 0 and 𝑎 . 𝑏 = 0, then what can be concluded about the vector 𝑏 ? Given, 𝑎. 𝑎 = 0 𝑎 𝑎 cos 0 = 0 𝑎2 cos 0 = 0 𝑎2 × 1 = 0 𝑎2 = 0 𝑎 = 0 So, 𝑎 = 0 Now it is given, 𝑎 . 𝑏 = 0 0 . 𝑏 = 0 is true, for any vector 𝑏 Therefore, if 𝑎 . 𝑎 = 0 and 𝑎 . 𝑏 = 0, then 𝑎 = 0 and 𝒃 can be any vector

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.