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Ex 10.3, 6 - Chapter 10 Class 12 Vector Algebra
Last updated at May 29, 2023 by Teachoo
Ex 10.3
Ex 10.3, 1
Ex 10.3, 2
Ex 10.3, 3 Important
Ex 10.3, 4
Ex 10.3, 5 Important
Ex 10.3, 6 You are here
Ex 10.3, 7
Ex 10.3, 8
Ex 10.3, 9 Important
Ex 10.3, 10 Important
Ex 10.3, 11
Ex 10.3, 12 Important
Ex 10.3, 13 Important
Ex 10.3, 14
Ex 10.3, 15 Important
Ex 10.3, 16 Important
Ex 10.3, 17
Ex 10.3, 18 (MCQ) Important
Transcript
Ex 10.3, 6 Find |𝑎 ⃗ | and |𝑏 ⃗ |, if (𝑎 ⃗ + b ⃗) .(𝑎 ⃗ – 𝑏 ⃗) = 8 and |𝑎 ⃗ | = 8 |𝑏 ⃗ | (𝑎 ⃗ + b ⃗) . (𝑎 ⃗ – 𝑏 ⃗) = 8 𝑎 ⃗.(𝑎 ⃗ – b ⃗) + 𝑏 ⃗.(𝑎 ⃗ − 𝑏 ⃗) = 8 𝑎 ⃗.𝑎 ⃗ − 𝑎 ⃗.𝑏 ⃗ + 𝒃 ⃗.𝒂 ⃗ − 𝑏 ⃗.𝑏 ⃗ = 8 𝑎 ⃗.𝑎 ⃗ − 𝑎 ⃗.𝑏 ⃗ + 𝒂 ⃗.𝒃 ⃗ − 𝑏 ⃗.𝑏 ⃗ = 8 𝒂 ⃗.𝒂 ⃗ − 𝒃 ⃗.𝒃 ⃗ = 8 |𝒂 ⃗ |2 – |𝒃 ⃗ |2 = 8 Also given that , |𝑎 ⃗ | = 8 |𝑏 ⃗ | Putting this in (1), |𝒂 ⃗ |2 – |𝑏 ⃗ |2 = 8 (Using prop: 𝑎 ⃗.𝑏 ⃗ = 𝑏 ⃗.𝑎 ⃗) (8|𝒃 ⃗ |)2 − |𝑏 ⃗ |2 = 8 64|𝑏 ⃗ |2 − |𝑏 ⃗ |2 = 8 63|𝑏 ⃗ |2 = 8 |𝑏 ⃗ |2 = 8/63 |𝑏 ⃗ | = √8/√63 ∴ |𝒃 ⃗ | = (𝟐 √𝟐)/(𝟑√𝟕) Also, |𝑎 ⃗ | = 8 × |𝑏 ⃗ | |𝑎 ⃗ | = 8 × (2 √2)/(3√7) ∴|𝒂 ⃗ | = (𝟏𝟔 √𝟐)/(𝟑√𝟕)
