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

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)

Let two non-collinear unit vector hat a a n d hat b form an acute angle. A point P moves so that at any time t , the position vector O P(w h e r eO is the origin ) is given by hat acost+ hat bsintdotW h e nP is farthest from origin O , let M be the length of O Pa n d hat u be the unit vector along O Pdot Then (a) hat u=( hat a+ hat b)/(| hat a+ hat b|)a n dM=(1+ hat adot hat b)^(1//2) (b) hat u=( hat a- hat b)/(| hat a- hat b|)a n dM=(1+ hat adot hat )^(1//2) (c) hat u=( hat a+ hat b)/(| hat a+ hat b|)a n dM=(1+2 hat adot hat b)^(1//2) (d) hat u=( hat a- hat b)/(| hat a- hat b|)a n dM=(1+2 hat adot hat b)^(1//2)

Let two non-collinear vectors veca and vecb inclined at an angle (2pi)/(3) be such that |veca|=3 and vec|b|=2 . If a point P moves so that at any time t its position vector vec(OP) (where O is the origin) is given as vec(OP) = (t+1/t)veca+(t-1/t)vecb then least distance of P from the origin is

Locus of the point P, for which vec(OP) represents a vector with direction cosine cos alpha = (1)/(2) (where O is the origin) is

A particle moves so that its position vector is given by vec r = cos omega t hat x + sin omega t hat y , where omega is a constant which of the following is true ?

A particle moves so that its position vector is given by vec r = cos omega t hat x + sin omega t hat y , where omega is a constant which of the following is true ?

If 2veca, 3vecb,2(veca xx vecb) are position vectors of the vectors A,B,C, of triangleABC and |veca|=|vecb|=1,vec(OA).vec(OB)=-3 (where O is the origin), then

A particle moves such that its momentum vector vecp(t) = cos omega t hati + sin omega t hatj where omega is a constant and t is time. Then which of the following statements is true for the velocity vec v(t) and acceleration veca (t) of the particle :

The position vectors of the points P and Q with respect to the origin O are veca = hati + 3hatj-2hatk and vecb = 3hati -hatj -2hatk , respectively. If M is a point on PQ, such that OM is the bisector of POQ, then vec(OM) is

The position vector sof points P,Q,R are 3veci+4vecj+5veck, 7veci-veck and 5veci+5vecj respectivley. If A is a point equidistant form the lines OP, OQ and OR find a unit vector along vec(OA) where O is the origin.