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

Let Two non-collinear vectors vec a and vec b inclined at angle of [2pi]/3 be such that |vec a|=3 and |vec b|=4.A point P moves so that at any time t the position vector vec [OP] (where O is the origin) is given as vec [OP]=(e^t+e^-t)vec a +(e^t-e^-t)vec b.If the least distance of P from the origin is sqrt2sqrt[sqrtp-q] where p,q in N,then find the value of p+q.

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

Let two non-collinear unit vectors hata and hatb form an 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 hata cos t + hatb sin t. When P is farthest from origin I, let M be the length of vec(OP) and hatu be teh unit vector along vec(OP). Then P:

Vectors veca and vec b are inclined at an angle theta = 120^@ . If |veca| = |vecb| = 2 , then [(veca + 3vecb) xx (3veca + vecb)]^2 is equal to

The vectors vec a and vecb are such that |vec a| = 2, |vec b| = 3, veca.vecb = 4 .Find |veca - vec b|

Let the vectors vec a and vec b be such that |veca| = 3 and |vecb| = (sqrt2)/(3) , then vec a xx vec b is a unit vector, if the angle between veca and vec b is

If veca and vecb are unit vectors, then angle between veca and vecb for sqrt3 ​ veca − vec b to be unit vector is

If veca and vecb are unit vectors, then angle between veca and vecb for sqrt3 ​ veca − vec b to be unit vector is