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Let two non-collinear unit vectors veca ...

Let two non-collinear unit vectors `veca and vecb` form an acute angle. A point P moves so that at any time t, time position vector, `vec(OP)` ( where O is the origin) is given by `hata cot t + hatb sin t`. When p is farthest fro origing o, let M be the length of `vec(OP) and hatu` be the unit vector along `vec(OP)` .then

A

`hatu =(hata + hatb)/(|hata +hatb|)` and `M=(1+hata.hatb)^(1/2)`

B

`hatu=(hata-hatb)/(|hata - hatb|)` and `M=(1+hata.hatb)^(1/2)`

C

`hatu =(hata +hatb)//(|hata + hatb|)` and `M=(1+2hata.hatb)^(1/2)`

D

`hatu =(hata -hatb)/(|hata -hatb|)` and `M=(1+2hata.hatb)^(1//2)`

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The correct Answer is:
A
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