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
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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 April 21, 2021 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)
