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Ex 10.3, 14 - If either a=0 or b=0, then a.b = 0, but converse - Scalar product - Defination

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Ex 10.3, 14 If either vector 𝑎﷯ = 0﷯ or 𝑏﷯ = 0﷯, then 𝑎﷯. 𝑏﷯ = 0 But the converse need not be true. justify your answer with an example. Converse: If 𝑎﷯ . 𝑏﷯ = 0, then either 𝑎﷯ = 0﷯ or 𝑏﷯ = 0﷯ Let 𝒂﷯ = 𝒊﷯ + 𝒋﷯ + 𝒌﷯ = 1 𝑖﷯ + 1 𝑗﷯ + 1 𝑘﷯ and 𝒃﷯ = 𝒊﷯ + 𝒋﷯ - 2 𝒌﷯ = 1 𝑖﷯ + 1 𝑗﷯ – 2 𝑘﷯ 𝑎﷯ . 𝑏﷯ = 1.1 + 1.1 + 1(−2) = 1 + 1 − 2 = 0 Hence, 𝑎﷯ . 𝑏﷯ = 0 but 𝑎﷯ ≠ 0﷯ and 𝑏﷯ ≠ 0﷯ Thus, the converse need not be true.

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