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Example 5 - Let a = i + 2j, b = 2i + j. Is |a| = |b|? - Examples

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Example 5 Let 𝑎﷯ = 𝑖﷯ + 2 𝑗﷯ and 𝑏﷯ = 2 𝑖﷯ + 𝑗﷯ . Is 𝑎﷯﷯ = 𝑏﷯﷯ ? Are the vectors 𝑎﷯ and 𝑏﷯ equal? 𝑎﷯ = 𝑖﷯ + 2 𝑗﷯ 𝑏﷯ = 2 𝑖﷯ + 𝑗﷯ We have, 𝑎﷯ = 1 𝑖﷯ + 2 𝑗﷯ + 0 𝑘﷯ and 𝑏﷯ = 2 𝑖﷯ + 1 𝑗﷯ + 0 𝑘﷯ Magnitude of 𝑎﷯ = ﷮12+22+02﷯ 𝑎﷯﷯ = ﷮1+4+0﷯ = ﷮5﷯ Magnitude of 𝑏﷯ = ﷮22+12+02﷯ 𝑏﷯﷯ = ﷮4+1+0﷯ = ﷮5﷯ So, 𝒂﷯﷯ = 𝒃﷯﷯ Now we have to check if 𝑎﷯ and 𝑏﷯ equal 𝑎﷯ = 1 𝑖﷯ + 2 𝑗﷯ + 0 𝑘﷯ & 𝑏﷯ = 2 𝑖﷯ + 1 𝑗﷯ + 0 𝑘﷯ Comparing corresponding components, As 1 ≠ 2 Thus, 𝑎﷯ and 𝑏﷯ are not equal since their corresponding components are distinct.

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