JEE Advanced 2008 Mathematics question

Let two non-collinear unit vectors and form an acute angle. A point P moves so that at any time t the position vector (where O is the origin) is given by . When P is farthest from origin O, let M be the length of and be the unit vector along . Then,

• (A) and Correct
• (B) and
• (C) and
• (D) and