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Given that a→.b→=0 and a→×b→=0 What can you conclude about the vectors anda→andb→? - Mathematics

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Question

Given that `veca.vecb = 0` and `veca xx vecb = 0` What can you conclude about the vectors `veca and vecb`?

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Solution

It is given that `veca xx vecb = 0, veca xx vecb = 0`

`|veca| = 0; |vecb| = 0; veca ⊥ vecb`

`veca xx vecb = 0`

`|veca| = 0, |vecb| = 0; |veca||vecb|`

`veca xx vecb = 0`

Either `veca = vec0` or `vecb = vec0`         ...[`veca ⊥ vecb "and"  veca | |vecb` are not valid at the same time]

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Chapter 10: Vector Algebra - Exercise 10.4 [Page 454]

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NCERT Mathematics [English] Class 12
Chapter 10 Vector Algebra
Exercise 10.4 | Q 6 | Page 454

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