`bara and barb` are two non-collinear vectors that the points with position vectors `l_1bara+m_1bar,l_2bara+m_2barb,l_2bara=m_3 barb`. Are collinear then find the value of `|:(1,1,1),(l_1,l_2,l_3),(m_1,m_2,m_3):|`

Three points whose position vectors are bara+barb,bara-barb and bara+kbarb are collinear, then the value of k is

If bara,barb,barc are non-coplanar vectors, then three points with position vectors bara-2barb+3barc,2bara+mbarb-4barc and -7barb+10barc will be collinear if m equals

If bara,barb and barc are non-coplanar vectors and the four points with position vectors 2bara+3barb-barc,bara-2barb+3barc,3bara+4barb-2barc,kbara-6barb+6barc are coplanar, then k

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

Three points having position vectors bara,barb and barc will be collinear if

If bara,barb,barc are non-zero, non collinear vectors, then the vectors bara-barb+barc,4bara-7barb-barc and 3bara+6barb+6barc are

If bara & barb are any two unit vectors then possible integers in the range of (3|bara+barb|)/2+2|bara-barb| is

If the points A,B,C and D have position vectors bara,2bara+barb,4bara+2barb and 5 bara+4barb respectively, then three collinear points are

If vec a and 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 det[[l_(1),m_(2),l_(3)m_(1),m_(2),m_(3)1,1,1]]=0

If bara,barb are non-collinear vectors and x,y are scalars such that (1bara-barb)x+(2barb-bara)y+(bara+2barb)=bar0 , then