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 \(\hat{a} \cos t+\hat{b} \sin t .\) When P is farthest from origin O, let M be the length of and be the unit vector along .
Then,

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 \(\hat{a} \cos t+\hat{b} \sin t .\) When P is farthest from origin O, let M be the length of

and

be the unit vector along

.
Then,

Accepted Answer

(A)

Let two non-collinear unit vectors and form an acute angle. A point P moves so that at…