Last updated at May 29, 2018 by Teachoo

Transcript

Example 18 If 𝑎 is a unit vector and ( 𝑥 − 𝑎) ⋅ ( 𝑥 + 𝑎) = 8 , then find | 𝑥| Given 𝑎 is a unit vector So, 𝑎 has a magnitude 1. ∴ 𝒂 = 1. Given that ( 𝑥 − 𝑎) ⋅ ( 𝑥 + 𝑎) = 8 𝑥 . 𝑥 + 𝑥 . 𝑎 − 𝒂 . 𝒙 − 𝑎 . 𝑎 = 8 𝑥 . 𝑥 + 𝑥 . 𝑎 − 𝒙 . 𝒂 − 𝑎 . 𝑎 = 8 𝒙 . 𝒙 − 𝒂 . 𝒂 = 8 𝒙2 − 𝒂2 = 8 𝑥2 − 12 = 8 𝑥2 = 8 + 1 𝑥2 = 9 𝑥 = ± 9 𝑥 = ± 3 Since magnitude is not negative, ∴ 𝒙 = 3

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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 9 years. He provides courses for Maths and Science at Teachoo.