Ex 10.3, 7 - Chapter 10 Class 12 Vector Algebra

Last updated at April 16, 2024 by

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

Transcript

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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.