Ex 10.3, 9 - Chapter 10 Class 12 Vector Algebra

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 𝒙﷯﷯2 − 𝒂﷯﷯2 = 12 𝑥﷯﷯2 − 12 = 12 𝑥﷯﷯2 = 12 + 1 𝑥﷯﷯2 = 13 𝑥﷯﷯ = ± ﷮13﷯ Since, magnitude of a vector is not negative, ∴ 𝒙﷯﷯ = ﷮𝟏𝟑﷯