Let two non-collinear unit vectors `hata and hatb` form an 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 `hata cos t + hatb sin t.` When P is farthest from origin I, let M be the length of `vec(OP) and hatu` be teh unit vector along `vec(OP).` Then P:

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

Answer

A