
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 10.3
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
Last updated at May 29, 2023 by Teachoo
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)