Check sibling questions

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


Transcript

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 ̂ = 1𝑖 ̂ + 1𝑗 ̂ + 1𝑘 ̂ and 𝒃 ⃗ = 𝒊 ̂ + 𝒋 ̂ - 2𝒌 ̂ = 1𝑖 ̂ + 1𝑗 ̂ – 2𝑘 ̂ 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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.