If ` vec aa n d vec b` are two non-collinear vectors, show that points `l_1 vec a+m_1 vec b ,l_2 vec a+m_2 vec b` and `l_3 vec a+m_3 vec b` are collinear if `|l_1l_2l_3m_1m_2m_3 1 1 1|=0.`

vec a and vec b are two non-collinear vectors. Show that the points with position vectors l_(1)vec a+m_(1)vec b,l_(2)vec a+m_(2)vec b,l_(3)vec b are collinear if l_(1)quad l_(2)quad l_(3)m_(1)quad m_(2)quad m_(3)]|=0

If vec a and vec b are two non collinear unit vectors such that |vec a+vec b|=3, find (2vec a-5vec b)3vec a+vec b

If vec a and vec b are two non-collinear unit vectors such that |vec a+vec b|=sqrt(3), find (2vec a-5vec b)*(3vec a+vec b)

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 vec a,vec b are two non-collinear vectors,prove that the points with position vectors vec a+vec b,vec a-vec b and vec a+lambdavec b are collinear for all real values of lambda

If vec a and vec b are two non-collinear vectors having the same initial point.What are the vectors represented by vec a+vec b and vec a-vec b

If vec a and vec b are non-collinear vectors,find the value of x for which the vectors vec alpha=(2x+1)vec a-vec b and vec beta=(x-2)vec a+vec b are collinear.

If vec a and vec b are non-collinear vectors,then the value of x for which vectors vec alpha=(x-2)vec a+vec b and vec beta=(3+2x)vec a-2vec b are collinear,is given by

If vec a, and vec b be two non-collinear unit vector such that vec a xx(vec a xxvec b)=(1)/(2)vec b, then find the angle between vec a, and vec b

vec a and vec b are two non-collinear vectors then |vec a+vec b+(vec a xxvec b)|^(2)+(1-vec a*vec b)^(2) is always equal to