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)`

Options

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

Answer

A