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. `hat(u)=(hat(a)+hat(b))/(|hat(a)+hat(b)|) and M=(1+hat(a)*hat(b))^((1)/(2))`
B. `hat(u)=(hat(a)-hat(b))/(|hat(a)-hat(b)|) and M=(1+hat(a)*hat(b))^((1)/(2))`
C. `hat(u)=(hat(a)+hat(b))/(|hat(a)+hat(b)|) and M=(1+2hat(a)*hat(b))^((1)/(2))`
D. `hat(u)=(hat(a)-hat(b))/(|hat(a)-hat(b)|) and M=(1+2hat(a)*hat(b))^((1)/(2))`

Answer

A