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

Example 18 - Chapter 10 Class 12 Vector Algebra - Part 2

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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 (Using: 𝑥 ⃗ . 𝑎 ⃗ = 𝑎 ⃗ . 𝑥 ⃗ ) |𝑥 ⃗ |2 = 8 + 1 |𝑥 ⃗ |2 = 9 |𝑥 ⃗ | = ± √9 |𝑥 ⃗ | = ± 3 Since magnitude is not negative, ∴ |𝒙 ⃗ | = 3

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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.