Example 5 - Chapter 10 Class 12 Vector Algebra
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 5 Let 𝑎 ⃗ = 𝑖 ̂ + 2𝑗 ̂ and 𝑏 ⃗ = 2𝑖 ̂ + 𝑗 ̂ . Is |𝑎 ⃗ | = |𝑏 ⃗ | ? Are the vectors 𝑎 ⃗ and 𝑏 ⃗ equal? Given 𝒂 ⃗ = 𝑖 ̂ + 2𝑗 ̂ & 𝒃 ⃗ = 2𝑖 ̂ + 𝑗 ̂ So, we can we can write, 𝒂 ⃗ = 1𝑖 ̂ + 2𝑗 ̂ + 0𝑘 ̂ & 𝒃 ⃗ = 2𝑖 ̂ + 1𝑗 ̂ + 0𝑘 ̂ Magnitude of 𝒂 ⃗ |𝑎 ⃗ | = √(12+22+02) = √5 Magnitude of 𝒃 ⃗ |𝑏 ⃗ | = √(22+12+02) = √5 Therefore, |𝒂 ⃗ | = |𝒃 ⃗ | Checking if 𝒂 ⃗ and 𝒃 ⃗ are equal 𝑎 ⃗ = 1𝑖 ̂ + 2𝑗 ̂ + 0𝑘 ̂ & 𝑏 ⃗ = 2𝑖 ̂ + 1𝑗 ̂ + 0𝑘 ̂ Comparing corresponding components, As 1 ≠ 2 Thus, 𝑎 ⃗ and 𝑏 ⃗ are not equal since their corresponding components are distinct.
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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