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why is vector division undefined?

why is vector division undefined?

Grade:11

4 Answers

Deepali Singh
32 Points
8 years ago

Division basically refers to multiplication of reciprocal. For example a/b is same as a*1/b or we can say, is same as a*b-1, which is "a" multiplied to the inverse of "b". There is no way of finding an inverse to a vector, and even if you could, you cant necessarily know if division in case of vectors implies left multiplication of inverse or right multiplication of inverse as we know that multiplication is not commutative in case of vectors i.e. AB≠BA where A,B are vectors. Hence, division of vectors is not defined.

If A and B are vectors, A/B could be AB-1 or it could be B-1A. Which way we mean isnt certain, and commutativity is an issue. And then finding b-1 is also an issue. Therefore A/B cannot be found out.

Kolla Raja Sekhar
51 Points
8 years ago

as a vector has direction

sai nath
33 Points
8 years ago

when direction can be multiplied.then it should also be divided.

KAPIL MANDAL
132 Points
6 years ago
Later in solid state physics, you will see it practically. 

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