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Keeping one vector constant, if directio...

Keeping one vector constant, if direction of other to be added in the first vector is changed continuously, tip of the resultant vector describes a circles, In the following figure vector `vec(a)` is kept constant. When vector `vec(b)` addede to `vec(a)` changes its direction, the tip of the resultant vector `vec(r)=vec(a)+vec(b)` describes circles of radius b with its centre at the tip of vector `vec(a)`. Maximum angle between vector `vec(a)` and the resultant `vec(r)=vec(a)+vec(b)` is

A

All three vectors must be parallel

B

`vec(b) and vec(c)` must be parallel to each other, but `vec(a)` need not be parallel to `vec(b) and vec(c)`

C

`vec(a) and vec(b)` must be perpendicular to each other

D

It is impossible for three non-zero vectors `vec(a), vec(b) and vec(c)` to have the property stated above

Text Solution

Verified by Experts

The correct Answer is:
D
Initially `a+b=c`
when `3a+ 2b= 2c`
`because c= a+b`
`therefore 3a+ 2b= 2(a+b) rArr a= 0`
Hence it is impossible for three non-zero vectors to have the property stated above
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