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Lelt two non collinear unit vectors hata...

Lelt two non collinear unit vectors `hata and hatb` form and acute angle. A point P moves so that at any time t the position vector `vec(OP)` (where O is the origin) is given by `hatacost+hatbsint.` When P is farthest from origin 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)`

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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