Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.3, 9 Find 𝑥, if for a unit vector 𝑎, ( 𝑥 − 𝑎).( 𝑥 + 𝑎) = 12. Given 𝑎 is a unit vector So, 𝑎 has a magnitude 1. ∴ 𝒂 = 1. Given that ( 𝑥 − 𝑎) ⋅ ( 𝑥 + 𝑎) = 12 𝑥 . 𝑥 + 𝑥 . 𝑎 − 𝒂 . 𝒙 − 𝑎 . 𝑎 = 12 𝑥 . 𝑥 + 𝑥 . 𝑎 − 𝒙 . 𝒂 − 𝑎 . 𝑎 = 12 𝒙 . 𝒙 − 𝒂 . 𝒂 = 12 𝒙2 − 𝒂2 = 12 𝑥2 − 12 = 12 𝑥2 = 12 + 1 𝑥2 = 13 𝑥 = ± 13 Since, magnitude of a vector is not negative, ∴ 𝒙 = 𝟏𝟑

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.