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

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Ex 10.3, 14 If either vector π‘Ž βƒ— = 0 βƒ— or 𝑏 βƒ— = 0 βƒ—, then π‘Ž βƒ—. 𝑏 βƒ— = 0 But the converse need not be true. justify your answer with an example. Converse: If π‘Ž βƒ— . 𝑏 βƒ— = 0, then either π‘Ž βƒ— = 0 βƒ— or 𝑏 βƒ— = 0 βƒ— Let 𝒂 βƒ— = π’Š Μ‚ + 𝒋 Μ‚ + π’Œ Μ‚ = 1𝑖 Μ‚ + 1𝑗 Μ‚ + 1π‘˜ Μ‚ and 𝒃 βƒ— = π’Š Μ‚ + 𝒋 Μ‚ - 2π’Œ Μ‚ = 1𝑖 Μ‚ + 1𝑗 Μ‚ – 2π‘˜ Μ‚ π‘Ž βƒ— . 𝑏 βƒ— = 1.1 + 1.1 + 1(βˆ’2) = 1 + 1 βˆ’ 2 = 0 Hence, π‘Ž βƒ— . 𝑏 βƒ— = 0 but π‘Ž βƒ— β‰  0 βƒ— and 𝑏 βƒ— β‰  0 βƒ— Thus, the converse need not be true.

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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.