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

  1. Chapter 10 Class 12 Vector Algebra (Term 2)
  2. Serial order wise

Transcript

Ex 10.3, 14 If either vector ๐‘Ž โƒ— = 0 โƒ— or ๐‘ โƒ— = 0 โƒ—, then ๐‘Ž โƒ—. ๐‘ โƒ— = 0 But the converse need not be true. justify your answer with an example. Converse: If ๐‘Ž โƒ— . ๐‘ โƒ— = 0, then either ๐‘Ž โƒ— = 0 โƒ— or ๐‘ โƒ— = 0 โƒ— Let ๐’‚ โƒ— = ๐’Š ฬ‚ + ๐’‹ ฬ‚ + ๐’Œ ฬ‚ = 1๐‘– ฬ‚ + 1๐‘— ฬ‚ + 1๐‘˜ ฬ‚ and ๐’ƒ โƒ— = ๐’Š ฬ‚ + ๐’‹ ฬ‚ - 2๐’Œ ฬ‚ = 1๐‘– ฬ‚ + 1๐‘— ฬ‚ โ€“ 2๐‘˜ ฬ‚ ๐‘Ž โƒ— . ๐‘ โƒ— = 1.1 + 1.1 + 1(โˆ’2) = 1 + 1 โˆ’ 2 = 0 Hence, ๐‘Ž โƒ— . ๐‘ โƒ— = 0 but ๐‘Ž โƒ— โ‰  0 โƒ— and ๐‘ โƒ— โ‰  0 โƒ— Thus, the converse need not be true.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.