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

Transcript

Ex 10.2, 19 If ๐‘Ž โƒ— and ๐‘ โƒ— are two collinear vectors, then which of the following are incorrect: (A) ๐‘ โƒ— = ฮป๐‘Ž โƒ—, for some scalar ฮป (B) ๐‘Ž โƒ— = ยฑ๐‘ โƒ— (C) the respective components of ๐‘Ž โƒ— and ๐‘ โƒ— are not proportional (D) both the vectors ๐‘Ž โƒ— and ๐‘ โƒ— have same direction, but different magnitudes. Given, a โƒ— and b โƒ— are collinear We need to check which case is always true Checking (A) ๐‘ โƒ— = ฮป๐‘Ž โƒ— If two vectors if a โƒ— and b โƒ— are collinear then b โƒ— = ฮป๐‘Ž โƒ— Where ฮป is any real number โˆด (A) is always correct Checking (B) ๐‘Ž โƒ— = ยฑ๐‘ โƒ— Let ๐‘Ž โƒ— = 1i ฬ‚ + 1j ฬ‚ + 1k ฬ‚ ๐‘ โƒ— = โˆ’3i ฬ‚ โˆ’ 3j ฬ‚ โˆ’ 3k ฬ‚ Here, ๐‘Ž โƒ— and ๐‘ โƒ— are collinear as direction ratios are proportional. But, ๐‘Ž โƒ— โ‰  ยฑ๐‘ โƒ— So, (B) is not always true Checking (C) (the respective components are not proportional) By definition of collinearity, if a โƒ— and b โƒ— are collinear then b โƒ— = ฮป๐‘Ž โƒ— Where ฮป is any real number Hence, the components of a โƒ— and b โƒ— are always proportional Hence, (C) is incorrect Checking (D) (both ๐‘Ž โƒ— and ๐‘ โƒ— have same direction, but different magnitudes) Let ๐‘Ž โƒ— = 1๐‘– ฬ‚ + 1๐‘— ฬ‚ + 1๐‘˜ ฬ‚ & ๐‘ โƒ— = โ€“3๐‘– ฬ‚ โ€“ 3๐‘— ฬ‚ โ€“ 3๐‘˜ ฬ‚ Here, a โƒ— & b โƒ— are collinear as direction ratios are in proportion. But, a โƒ— and ๐‘ โƒ— have opposite direction โˆด (D) is not always true So, (B), (C), (D) are incorrect

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.