Example 18 - lf a is a unit vector (x - a) . (x + a) = 8, find x - Examples

Slide40.JPG

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
Ask Download

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 𝒙﷯﷯2 − 𝒂﷯﷯2 = 8 𝑥﷯﷯2 − 12 = 8 𝑥﷯﷯2 = 8 + 1 𝑥﷯﷯2 = 9 𝑥﷯﷯ = ± ﷮9﷯ 𝑥﷯﷯ = ± 3 Since magnitude is not negative, ∴ 𝒙﷯﷯ = 3

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.