Ex 10.3, 9 - Find |x| if for a unit vector a,(x - a).(x + a)= 12

Ex 10.3, 9 - Chapter 10 Class 12 Vector Algebra - Part 2

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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 (Using prop : 𝑥 ⃗ . 𝑎 ⃗ = 𝑎 ⃗ . 𝑥 ⃗ ) |𝑥 ⃗ |2 = 13 |𝑥 ⃗ | = ± √13 Since, magnitude of a vector is not negative, ∴ |𝒙 ⃗ | = √𝟏𝟑

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.