IF `veca and vecb` are no collinear vectors and `vecA=(x+4y)veca+(2x+y+1)vecb and vecB=(y-2x+2)vec+(2x-3y-1)vecb,` find x and y such that `3vecA=2vecB`.

If veca and vecb are non-collinear vectors and vecA= (p+4q)veca+ (2p+q+1)vecb and vecB= (-2p+q+2)veca+ (2p-3q-1)vecb , and if 3vecA= 2vecB , then determine p and q .

If veca and vecb are non - zero vectors such that |veca + vecb| = |veca - 2vecb| then

Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(veca.vecb)vecb and vec=vecaxxvecb , then |vecv| is

If veca and vecb are two non collinear unit vectors and |veca+vecb|= sqrt3 , then find the value of (veca- vecb)*(2veca+ vecb)

If veca and vecb are two non collinear unit vectors and iveca+vecbi=sqrt(3) then find the value of (veca-vecb).(2veca+vecb)

vecb and vecc are non- collinear if veca xx (vecb xx vecc) + (veca .vecb) vecb = ( 4-2x- sin y) vecb + ( x^(2) -1) vecc andd (vec. vecc) veca =veca then

The vectors veca and vecb are non collinear. Find for what value of x the vectors vecc=(x-2)veca+vecb and vecd=(2x+1) veca-vecb are collinear.?

Statement -1 : If veca and vecb are non- collinear vectors, then points having position vectors x_(1) vec(a) + y_(1) vec(b) , x_(2)vec(a)+ y_(2) vec(b) and x_(3) veca + y_(3) vecb are collinear if |(x_(1),x_(2),x_(3)),(y_(1),y_(2),y_(3)),(1,1,1)|=0 Statement -2: Three points with position vectors veca, vecb , vec c are collinear iff there exist scalars x, y, z not all zero such that x vec a + y vec b + z vec c = vec 0, " where " x+y+z=0.

If veca , vecb are unit vectors such that |vec a+vecb|=-1 " then " |2veca -3vecb| =