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If vec(c )=vec(a)-vec(b), which of the f...

If `vec(c )=vec(a)-vec(b)`, which of the following relations among magnitudes cannot be achieved by any choice of `vec(a)` and `vec(b)` ?

A

`c=a-b`

B

`c gt a, c gt b`

C

`c=a+b`

D

`c lt a-b`

Text Solution

Verified by Experts

The correct Answer is:
D
`vec(c )=vec(a)-vec(b) rArrc=sqrt(a^(2)+b^(2)-2ab cos theta)`
hence `c_(min)=a-b`
and `c` can not be less than `a-b`
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