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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo