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Last updated at Jan. 31, 2020 by Teachoo

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Ex 10.2, 19 If ๐ โ and ๐ โ are two collinear vectors, then which of the following are incorrect: (A) ๐ โ = ฮป๐ โ, for some scalar ฮป (B) ๐ โ = ยฑ๐ โ (C) the respective components of ๐ โ and ๐ โ are not proportional (D) both the vectors ๐ โ and ๐ โ have same direction, but different magnitudes. Given, a โ and b โ are collinear We need to check which case is always true Checking (A) ๐ โ = ฮป๐ โ If two vectors if a โ and b โ are collinear then b โ = ฮป๐ โ Where ฮป is any real number โด (A) is always correct Checking (B) ๐ โ = ยฑ๐ โ Let ๐ โ = 1i ฬ + 1j ฬ + 1k ฬ ๐ โ = โ3i ฬ โ 3j ฬ โ 3k ฬ Here, ๐ โ and ๐ โ are collinear as direction ratios are proportional. But, ๐ โ โ ยฑ๐ โ So, (B) is not always true Checking (C) (the respective components are not proportional) By definition of collinearity, if a โ and b โ are collinear then b โ = ฮป๐ โ Where ฮป is any real number Hence, the components of a โ and b โ are always proportional Hence, (C) is incorrect Checking (D) (both ๐ โ and ๐ โ have same direction, but different magnitudes) Let ๐ โ = 1๐ ฬ + 1๐ ฬ + 1๐ ฬ & ๐ โ = โ3๐ ฬ โ 3๐ ฬ โ 3๐ ฬ Here, a โ & b โ are collinear as direction ratios are in proportion. But, a โ and ๐ โ have opposite direction โด (D) is not always true So, (B), (C), (D) are incorrect

Ex 10.2

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About the Author

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.