Ex 10.3, 7 - Chapter 10 Class 12 Vector Algebra

Last updated at Dec. 16, 2024 by

Ex 10.3, 7 - Evaluate product (3a - 5b).(2a + 7b) - Class 12

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Ex 10.3, 7 Evaluate the product (3𝑎 ⃗ − 5𝑏 ⃗) ⋅ (2𝑎 ⃗ + 7𝑏 ⃗). (3𝑎 ⃗ − 5𝑏 ⃗) ⋅ (2𝑎 ⃗ + 7𝑏 ⃗) = 3𝑎 ⃗ . 2𝑎 ⃗ + 3𝑎 ⃗.7𝑏 ⃗ − 5𝑏 ⃗.2𝑎 ⃗ − 5𝑏 ⃗. 7𝑏 ⃗ = 6(𝑎 ⃗. 𝑎 ⃗) + 21(𝑎 ⃗. 𝑏 ⃗) − 10 (𝒃 ⃗. 𝒂 ⃗) − 35 (𝑏 ⃗. 𝑏 ⃗) = 6(𝑎 ⃗. 𝑎 ⃗) + 21(𝑎 ⃗. 𝑏 ⃗) − 10 (𝒂 ⃗. 𝒃 ⃗) − 35 (𝑏 ⃗. 𝑏 ⃗) = 6(𝒂 ⃗. 𝒂 ⃗) + 11 (𝑎 ⃗. 𝑏 ⃗) −35 (𝒃 ⃗. 𝒃 ⃗) = 6 |𝒂 ⃗ |2 + 11(𝑎 ⃗. 𝑏 ⃗) − 35 |𝒃 ⃗ |2 Therefore, (3𝑎 ⃗ − 5𝑏 ⃗) ⋅ (2𝑎 ⃗ + 7𝑏 ⃗) = 6|𝒂 ⃗ |2 + 11 (𝒂 ⃗. 𝒃 ⃗) − 35 |𝒃 ⃗ |2

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