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

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